6x^2-80x=-38

Solution for 6x^2-80x=-38 equation:

6x^2-80x=-38

We move all terms to the left:

6x^2-80x-(-38)=0

We add all the numbers together, and all the variables

6x^2-80x+38=0

a = 6; b = -80; c = +38;
Δ = b2-4ac
Δ = -802-4·6·38
Δ = 5488
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:

$\sqrt{\Delta}=\sqrt{5488}=\sqrt{784*7}=\sqrt{784}*\sqrt{7}=28\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-28\sqrt{7}}{2*6}=\frac{80-28\sqrt{7}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+28\sqrt{7}}{2*6}=\frac{80+28\sqrt{7}}{12}
$