64=30x+x^2

Solution for 64=30x+x^2 equation:

64=30x+x^2

We move all terms to the left:

64-(30x+x^2)=0

We get rid of parentheses

-x^2-30x+64=0

We add all the numbers together, and all the variables

-1x^2-30x+64=0

a = -1; b = -30; c = +64;
Δ = b2-4ac
Δ = -302-4·(-1)·64
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-34}{2*-1}=\frac{-4}{-2}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+34}{2*-1}=\frac{64}{-2}
=-32
$