-2x(x+6)+3=6(x+2)+8

Solution for -2x(x+6)+3=6(x+2)+8 equation:

-2x(x+6)+3=6(x+2)+8

We move all terms to the left:

-2x(x+6)+3-(6(x+2)+8)=0

We multiply parentheses

-2x^2-12x-(6(x+2)+8)+3=0


We calculate terms in parentheses: -(6(x+2)+8), so:

6(x+2)+8

We multiply parentheses

6x+12+8

We add all the numbers together, and all the variables

6x+20

Back to the equation:

-(6x+20)


We get rid of parentheses

-2x^2-12x-6x-20+3=0

We add all the numbers together, and all the variables

-2x^2-18x-17=0

a = -2; b = -18; c = -17;
Δ = b2-4ac
Δ = -182-4·(-2)·(-17)
Δ = 188
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:

$\sqrt{\Delta}=\sqrt{188}=\sqrt{4*47}=\sqrt{4}*\sqrt{47}=2\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{47}}{2*-2}=\frac{18-2\sqrt{47}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{47}}{2*-2}=\frac{18+2\sqrt{47}}{-4}
$