Solve Using the Quadratic Formula 4x^2+10x-13=5x

$4 x^{2} + 10 x - 13 = 5 x$

Step 1

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

Subtract $5 x$ from both sides of the equation.

$4 x^{2} + 10 x - 13 - 5 x = 0$

Subtract $5 x$ from $10 x$ .

$4 x^{2} + 5 x - 13 = 0$

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 $a = 4$ , $b = 5$ , and $c = - 13$ into the quadratic formula and solve for $x$ .

$\frac{- 5 \pm \sqrt{5^{2} - 4 \cdot (4 \cdot - 13)}}{2 \cdot 4}$

Step 4

Simplify.

Simplify the numerator.

Raise $5$ to the power of $2$ .

$x = \frac{- 5 \pm \sqrt{25 - 4 \cdot 4 \cdot - 13}}{2 \cdot 4}$

Multiply $- 4 \cdot 4 \cdot - 13$ .

Multiply $- 4$ by $4$ .

$x = \frac{- 5 \pm \sqrt{25 - 16 \cdot - 13}}{2 \cdot 4}$

Multiply $- 16$ by $- 13$ .

$x = \frac{- 5 \pm \sqrt{25 + 208}}{2 \cdot 4}$

Add $25$ and $208$ .

$x = \frac{- 5 \pm \sqrt{233}}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{- 5 \pm \sqrt{233}}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 5 \pm \sqrt{233}}{8}$

Decimal Form:

$x = 1.28304219 \dots, - 2.53304219 \dots$