79-3x^2-8x=5

Solution for 79-3x^2-8x=5 equation:

79-3x^2-8x=5

We move all terms to the left:

79-3x^2-8x-(5)=0

We add all the numbers together, and all the variables

-3x^2-8x+74=0

a = -3; b = -8; c = +74;
Δ = b2-4ac
Δ = -82-4·(-3)·74
Δ = 952
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:

$\sqrt{\Delta}=\sqrt{952}=\sqrt{4*238}=\sqrt{4}*\sqrt{238}=2\sqrt{238}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{238}}{2*-3}=\frac{8-2\sqrt{238}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{238}}{2*-3}=\frac{8+2\sqrt{238}}{-6}
$