(5x-4)(5x-4)-(3x+5)(2x-1)=20x(x-2)+27

Solution for (5x-4)(5x-4)-(3x+5)(2x-1)=20x(x-2)+27 equation:

(5x-4)(5x-4)-(3x+5)(2x-1)=20x(x-2)+27

We move all terms to the left:

(5x-4)(5x-4)-(3x+5)(2x-1)-(20x(x-2)+27)=0

We multiply parentheses ..

(+25x^2-20x-20x+16)-(3x+5)(2x-1)-(20x(x-2)+27)=0


We calculate terms in parentheses: -(20x(x-2)+27), so:

20x(x-2)+27

We multiply parentheses

20x^2-40x+27

Back to the equation:

-(20x^2-40x+27)


We get rid of parentheses

25x^2-20x^2-20x-20x-(3x+5)(2x-1)+40x+16-27=0

We multiply parentheses ..

25x^2-20x^2-(+6x^2-3x+10x-5)-20x-20x+40x+16-27=0

We add all the numbers together, and all the variables

5x^2-(+6x^2-3x+10x-5)-11=0

We get rid of parentheses

5x^2-6x^2+3x-10x+5-11=0

We add all the numbers together, and all the variables

-1x^2-7x-6=0

a = -1; b = -7; c = -6;
Δ = b2-4ac
Δ = -72-4·(-1)·(-6)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-5}{2*-1}=\frac{2}{-2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+5}{2*-1}=\frac{12}{-2}
=-6
$