(x-3)(60+2x)=63x

Solution for (x-3)(60+2x)=63x equation:

(x-3)(60+2x)=63x

We move all terms to the left:

(x-3)(60+2x)-(63x)=0

We add all the numbers together, and all the variables

(x-3)(2x+60)-63x=0

We add all the numbers together, and all the variables

-63x+(x-3)(2x+60)=0

We multiply parentheses ..

(+2x^2+60x-6x-180)-63x=0

We get rid of parentheses

2x^2+60x-6x-63x-180=0

We add all the numbers together, and all the variables

2x^2-9x-180=0

a = 2; b = -9; c = -180;
Δ = b2-4ac
Δ = -92-4·2·(-180)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-39}{2*2}=\frac{-30}{4}
=-7+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+39}{2*2}=\frac{48}{4}
=12
$