6x(x+5)+8=2

Solution for 6x(x+5)+8=2 equation:

6x(x+5)+8=2

We move all terms to the left:

6x(x+5)+8-(2)=0

We add all the numbers together, and all the variables

6x(x+5)+6=0

We multiply parentheses

6x^2+30x+6=0

a = 6; b = 30; c = +6;
Δ = b2-4ac
Δ = 302-4·6·6
Δ = 756
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:

$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{21}}{2*6}=\frac{-30-6\sqrt{21}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{21}}{2*6}=\frac{-30+6\sqrt{21}}{12}
$