(x-6)(5x+3)=(2x-6)(2x-6)

Solution for (x-6)(5x+3)=(2x-6)(2x-6) equation:

(x-6)(5x+3)=(2x-6)(2x-6)

We move all terms to the left:

(x-6)(5x+3)-((2x-6)(2x-6))=0

We multiply parentheses ..

(+5x^2+3x-30x-18)-((2x-6)(2x-6))=0


We calculate terms in parentheses: -((2x-6)(2x-6)), so:

(2x-6)(2x-6)

We multiply parentheses ..

(+4x^2-12x-12x+36)

We get rid of parentheses

4x^2-12x-12x+36

We add all the numbers together, and all the variables

4x^2-24x+36

Back to the equation:

-(4x^2-24x+36)


We get rid of parentheses

5x^2-4x^2+3x-30x+24x-18-36=0

We add all the numbers together, and all the variables

x^2-3x-54=0

a = 1; b = -3; c = -54;
Δ = b2-4ac
Δ = -32-4·1·(-54)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-15}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+15}{2*1}=\frac{18}{2}
=9
$