(X-1)-5(x-2)-(2x+3)-(5x+2)(x-1)=0

Solution for (X-1)-5(x-2)-(2x+3)-(5x+2)(x-1)=0 equation:

(X-1)-5(X-2)-(2X+3)-(5X+2)(X-1)=0

We multiply parentheses

(X-1)-5X-(2X+3)-(5X+2)(X-1)+10=0

We get rid of parentheses

X-5X-2X-(5X+2)(X-1)-1-3+10=0

We multiply parentheses ..

-(+5X^2-5X+2X-2)+X-5X-2X-1-3+10=0

We add all the numbers together, and all the variables

-(+5X^2-5X+2X-2)-6X+6=0

We get rid of parentheses

-5X^2+5X-2X-6X+2+6=0

We add all the numbers together, and all the variables

-5X^2-3X+8=0

a = -5; b = -3; c = +8;
Δ = b2-4ac
Δ = -32-4·(-5)·8
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-13}{2*-5}=\frac{-10}{-10}
=1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+13}{2*-5}=\frac{16}{-10}
=-1+3/5
$