8=2(x-5)6x

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

8=2(x-5)6x

We move all terms to the left:

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


We calculate terms in parentheses: -(2(x-5)6x), so:

2(x-5)6x

We multiply parentheses

12x^2-60x

Back to the equation:

-(12x^2-60x)


We get rid of parentheses

-12x^2+60x+8=0

a = -12; b = 60; c = +8;
Δ = b2-4ac
Δ = 602-4·(-12)·8
Δ = 3984
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:

$\sqrt{\Delta}=\sqrt{3984}=\sqrt{16*249}=\sqrt{16}*\sqrt{249}=4\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{249}}{2*-12}=\frac{-60-4\sqrt{249}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{249}}{2*-12}=\frac{-60+4\sqrt{249}}{-24}
$