2(x-2)-5x(x-5)=4(x-8)-2(x-2)

Solution for 2(x-2)-5x(x-5)=4(x-8)-2(x-2) equation:

2(x-2)-5x(x-5)=4(x-8)-2(x-2)

We move all terms to the left:

2(x-2)-5x(x-5)-(4(x-8)-2(x-2))=0

We multiply parentheses

-5x^2+2x+25x-(4(x-8)-2(x-2))-4=0


We calculate terms in parentheses: -(4(x-8)-2(x-2)), so:

4(x-8)-2(x-2)

We multiply parentheses

4x-2x-32+4

We add all the numbers together, and all the variables

2x-28

Back to the equation:

-(2x-28)


We add all the numbers together, and all the variables

-5x^2+27x-(2x-28)-4=0

We get rid of parentheses

-5x^2+27x-2x+28-4=0

We add all the numbers together, and all the variables

-5x^2+25x+24=0

a = -5; b = 25; c = +24;
Δ = b2-4ac
Δ = 252-4·(-5)·24
Δ = 1105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-\sqrt{1105}}{2*-5}=\frac{-25-\sqrt{1105}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{1105}}{2*-5}=\frac{-25+\sqrt{1105}}{-10}
$