x^2-46x=-60

Solution for x^2-46x=-60 equation:

x^2-46x=-60

We move all terms to the left:

x^2-46x-(-60)=0

We add all the numbers together, and all the variables

x^2-46x+60=0

a = 1; b = -46; c = +60;
Δ = b2-4ac
Δ = -462-4·1·60
Δ = 1876
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:

$\sqrt{\Delta}=\sqrt{1876}=\sqrt{4*469}=\sqrt{4}*\sqrt{469}=2\sqrt{469}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{469}}{2*1}=\frac{46-2\sqrt{469}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{469}}{2*1}=\frac{46+2\sqrt{469}}{2}
$