8=5(x+6)x

Solution for 8=5(x+6)x equation:

8=5(x+6)x

We move all terms to the left:

8-(5(x+6)x)=0


We calculate terms in parentheses: -(5(x+6)x), so:

5(x+6)x

We multiply parentheses

5x^2+30x

Back to the equation:

-(5x^2+30x)


We get rid of parentheses

-5x^2-30x+8=0

a = -5; b = -30; c = +8;
Δ = b2-4ac
Δ = -302-4·(-5)·8
Δ = 1060
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:

$\sqrt{\Delta}=\sqrt{1060}=\sqrt{4*265}=\sqrt{4}*\sqrt{265}=2\sqrt{265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{265}}{2*-5}=\frac{30-2\sqrt{265}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{265}}{2*-5}=\frac{30+2\sqrt{265}}{-10}
$