(3x+5)(x-5)=12x+20

Solution for (3x+5)(x-5)=12x+20 equation:

(3x+5)(x-5)=12x+20

We move all terms to the left:

(3x+5)(x-5)-(12x+20)=0

We get rid of parentheses

(3x+5)(x-5)-12x-20=0

We multiply parentheses ..

(+3x^2-15x+5x-25)-12x-20=0

We get rid of parentheses

3x^2-15x+5x-12x-25-20=0

We add all the numbers together, and all the variables

3x^2-22x-45=0

a = 3; b = -22; c = -45;
Δ = b2-4ac
Δ = -222-4·3·(-45)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-32}{2*3}=\frac{-10}{6}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+32}{2*3}=\frac{54}{6}
=9
$