4x^2-24x-9=-10x

Solution for 4x^2-24x-9=-10x equation:

4x^2-24x-9=-10x

We move all terms to the left:

4x^2-24x-9-(-10x)=0

We get rid of parentheses

4x^2-24x+10x-9=0

We add all the numbers together, and all the variables

4x^2-14x-9=0

a = 4; b = -14; c = -9;
Δ = b2-4ac
Δ = -142-4·4·(-9)
Δ = 340
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{85}}{2*4}=\frac{14-2\sqrt{85}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{85}}{2*4}=\frac{14+2\sqrt{85}}{8}
$