-2x(x+10)=3(-5x-8)

Solution for -2x(x+10)=3(-5x-8) equation:

-2x(x+10)=3(-5x-8)

We move all terms to the left:

-2x(x+10)-(3(-5x-8))=0

We multiply parentheses

-2x^2-20x-(3(-5x-8))=0


We calculate terms in parentheses: -(3(-5x-8)), so:

3(-5x-8)

We multiply parentheses

-15x-24

Back to the equation:

-(-15x-24)


We get rid of parentheses

-2x^2-20x+15x+24=0

We add all the numbers together, and all the variables

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

a = -2; b = -5; c = +24;
Δ = b2-4ac
Δ = -52-4·(-2)·24
Δ = 217
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{-(-5)-\sqrt{217}}{2*-2}=\frac{5-\sqrt{217}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{217}}{2*-2}=\frac{5+\sqrt{217}}{-4}
$