3x2+64=33x-8

Solution for 3x2+64=33x-8 equation:

3x^2+64=33x-8

We move all terms to the left:

3x^2+64-(33x-8)=0

We get rid of parentheses

3x^2-33x+8+64=0

We add all the numbers together, and all the variables

3x^2-33x+72=0

a = 3; b = -33; c = +72;
Δ = b2-4ac
Δ = -332-4·3·72
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-15}{2*3}=\frac{18}{6}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+15}{2*3}=\frac{48}{6}
=8
$