-2(3x-5)=4x(x+3)+8

Solution for -2(3x-5)=4x(x+3)+8 equation:

-2(3x-5)=4x(x+3)+8

We move all terms to the left:

-2(3x-5)-(4x(x+3)+8)=0

We multiply parentheses

-6x-(4x(x+3)+8)+10=0


We calculate terms in parentheses: -(4x(x+3)+8), so:

4x(x+3)+8

We multiply parentheses

4x^2+12x+8

Back to the equation:

-(4x^2+12x+8)


We get rid of parentheses

-4x^2-6x-12x-8+10=0

We add all the numbers together, and all the variables

-4x^2-18x+2=0

a = -4; b = -18; c = +2;
Δ = b2-4ac
Δ = -182-4·(-4)·2
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{89}}{2*-4}=\frac{18-2\sqrt{89}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{89}}{2*-4}=\frac{18+2\sqrt{89}}{-8}
$