-2x(x+10)=3(2x-4)

Solution for -2x(x+10)=3(2x-4) equation:

-2x(x+10)=3(2x-4)

We move all terms to the left:

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

We multiply parentheses

-2x^2-20x-(3(2x-4))=0


We calculate terms in parentheses: -(3(2x-4)), so:

3(2x-4)

We multiply parentheses

6x-12

Back to the equation:

-(6x-12)


We get rid of parentheses

-2x^2-20x-6x+12=0

We add all the numbers together, and all the variables

-2x^2-26x+12=0

a = -2; b = -26; c = +12;
Δ = b2-4ac
Δ = -262-4·(-2)·12
Δ = 772
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:

$\sqrt{\Delta}=\sqrt{772}=\sqrt{4*193}=\sqrt{4}*\sqrt{193}=2\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{193}}{2*-2}=\frac{26-2\sqrt{193}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{193}}{2*-2}=\frac{26+2\sqrt{193}}{-4}
$