2(x-1)(x-2)=(x-5)(x+4)+5x

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

2(x-1)(x-2)=(x-5)(x+4)+5x

We move all terms to the left:

2(x-1)(x-2)-((x-5)(x+4)+5x)=0

We multiply parentheses ..

2(+x^2-2x-1x+2)-((x-5)(x+4)+5x)=0


We calculate terms in parentheses: -((x-5)(x+4)+5x), so:

(x-5)(x+4)+5x

We add all the numbers together, and all the variables

5x+(x-5)(x+4)

We multiply parentheses ..

(+x^2+4x-5x-20)+5x

We get rid of parentheses

x^2+4x-5x+5x-20

We add all the numbers together, and all the variables

x^2+4x-20

Back to the equation:

-(x^2+4x-20)


We multiply parentheses

2x^2-4x-2x-(x^2+4x-20)+4=0

We get rid of parentheses

2x^2-x^2-4x-2x-4x+20+4=0

We add all the numbers together, and all the variables

x^2-10x+24=0

a = 1; b = -10; c = +24;
Δ = b2-4ac
Δ = -102-4·1·24
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2}{2*1}=\frac{8}{2}
=4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2}{2*1}=\frac{12}{2}
=6
$