6x^2-51x+32=8

Solution for 6x^2-51x+32=8 equation:

6x^2-51x+32=8

We move all terms to the left:

6x^2-51x+32-(8)=0

We add all the numbers together, and all the variables

6x^2-51x+24=0

a = 6; b = -51; c = +24;
Δ = b2-4ac
Δ = -512-4·6·24
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-45}{2*6}=\frac{6}{12}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+45}{2*6}=\frac{96}{12}
=8
$