7x^2-12x-5=x^2+20x

Solution for 7x^2-12x-5=x^2+20x equation:

7x^2-12x-5=x^2+20x

We move all terms to the left:

7x^2-12x-5-(x^2+20x)=0

We get rid of parentheses

7x^2-x^2-12x-20x-5=0

We add all the numbers together, and all the variables

6x^2-32x-5=0

a = 6; b = -32; c = -5;
Δ = b2-4ac
Δ = -322-4·6·(-5)
Δ = 1144
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:

$\sqrt{\Delta}=\sqrt{1144}=\sqrt{4*286}=\sqrt{4}*\sqrt{286}=2\sqrt{286}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{286}}{2*6}=\frac{32-2\sqrt{286}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{286}}{2*6}=\frac{32+2\sqrt{286}}{12}
$