20x^2+12x-15x+9=24x^2-8x-21x+7

Solution for 20x^2+12x-15x+9=24x^2-8x-21x+7 equation:

20x^2+12x-15x+9=24x^2-8x-21x+7

We move all terms to the left:

20x^2+12x-15x+9-(24x^2-8x-21x+7)=0

We add all the numbers together, and all the variables

20x^2-3x-(24x^2-8x-21x+7)+9=0

We get rid of parentheses

20x^2-24x^2-3x+8x+21x-7+9=0

We add all the numbers together, and all the variables

-4x^2+26x+2=0

a = -4; b = 26; c = +2;
Δ = b2-4ac
Δ = 262-4·(-4)·2
Δ = 708
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:

$\sqrt{\Delta}=\sqrt{708}=\sqrt{4*177}=\sqrt{4}*\sqrt{177}=2\sqrt{177}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{177}}{2*-4}=\frac{-26-2\sqrt{177}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{177}}{2*-4}=\frac{-26+2\sqrt{177}}{-8}
$