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

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

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

We move all terms to the left:

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

We multiply parentheses

5(x-5)(x-2)-2x-(3(x-5))+4=0

We multiply parentheses ..

5(+x^2-2x-5x+10)-2x-(3(x-5))+4=0


We calculate terms in parentheses: -(3(x-5)), so:

3(x-5)

We multiply parentheses

3x-15

Back to the equation:

-(3x-15)


We multiply parentheses

5x^2-10x-25x-2x-(3x-15)+50+4=0

We get rid of parentheses

5x^2-10x-25x-2x-3x+15+50+4=0

We add all the numbers together, and all the variables

5x^2-40x+69=0

a = 5; b = -40; c = +69;
Δ = b2-4ac
Δ = -402-4·5·69
Δ = 220
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{55}}{2*5}=\frac{40-2\sqrt{55}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{55}}{2*5}=\frac{40+2\sqrt{55}}{10}
$