x^2-64=12(12+15)

Solution for x^2-64=12(12+15) equation:

x^2-64=12(12+15)

We move all terms to the left:

x^2-64-(12(12+15))=0

We add all the numbers together, and all the variables

x^2-64-(1227)=0

We add all the numbers together, and all the variables

x^2-1291=0

a = 1; b = 0; c = -1291;
Δ = b2-4ac
Δ = 02-4·1·(-1291)
Δ = 5164
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:

$\sqrt{\Delta}=\sqrt{5164}=\sqrt{4*1291}=\sqrt{4}*\sqrt{1291}=2\sqrt{1291}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{1291}}{2*1}=\frac{0-2\sqrt{1291}}{2}
=-\frac{2\sqrt{1291}}{2}
=-\sqrt{1291}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{1291}}{2*1}=\frac{0+2\sqrt{1291}}{2}
=\frac{2\sqrt{1291}}{2}
=\sqrt{1291}
$