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

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

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(5(-3x+4)), so:

5(-3x+4)

We multiply parentheses

-15x+20

Back to the equation:

-(-15x+20)


We get rid of parentheses

-2x^2+10x+15x-20=0

We add all the numbers together, and all the variables

-2x^2+25x-20=0

a = -2; b = 25; c = -20;
Δ = b2-4ac
Δ = 252-4·(-2)·(-20)
Δ = 465
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{465}}{2*-2}=\frac{-25-\sqrt{465}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{465}}{2*-2}=\frac{-25+\sqrt{465}}{-4}
$