Solve Using the Quadratic Formula 42x^2-69x+20=7x^2-8

$42 x^{2} - 69 x + 20 = 7 x^{2} - 8$

Step 1

Move all terms to the left side of the equation and simplify.

Move all the expressions to the left side of the equation.

Subtract $7 x^{2}$ from both sides of the equation.

$42 x^{2} - 69 x + 20 - 7 x^{2} = - 8$

Add $8$ to both sides of the equation.

$42 x^{2} - 69 x + 20 - 7 x^{2} + 8 = 0$

Simplify $42 x^{2} - 69 x + 20 - 7 x^{2} + 8$ .

Subtract $7 x^{2}$ from $42 x^{2}$ .

$35 x^{2} - 69 x + 20 + 8 = 0$

Add $20$ and $8$ .

$35 x^{2} - 69 x + 28 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 35$ , $b = - 69$ , and $c = 28$ into the quadratic formula and solve for $x$ .

$\frac{69 \pm \sqrt{{(- 69)}^{2} - 4 \cdot (35 \cdot 28)}}{2 \cdot 35}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 69$ to the power of $2$ .

$x = \frac{69 \pm \sqrt{4761 - 4 \cdot 35 \cdot 28}}{2 \cdot 35}$

Multiply $- 4 \cdot 35 \cdot 28$ .

Multiply $- 4$ by $35$ .

$x = \frac{69 \pm \sqrt{4761 - 140 \cdot 28}}{2 \cdot 35}$

Multiply $- 140$ by $28$ .

$x = \frac{69 \pm \sqrt{4761 - 3920}}{2 \cdot 35}$

Subtract $3920$ from $4761$ .

$x = \frac{69 \pm \sqrt{841}}{2 \cdot 35}$

Rewrite $841$ as $29^{2}$ .

$x = \frac{69 \pm \sqrt{29^{2}}}{2 \cdot 35}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{69 \pm 29}{2 \cdot 35}$

Multiply $2$ by $35$ .

$x = \frac{69 \pm 29}{70}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{7}{5}, \frac{4}{7}$