48x-13=-x^2

Solution for 48x-13=-x^2 equation:

48x-13=-x^2

We move all terms to the left:

48x-13-(-x^2)=0

We get rid of parentheses

x^2+48x-13=0

a = 1; b = 48; c = -13;
Δ = b2-4ac
Δ = 482-4·1·(-13)
Δ = 2356
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:

$\sqrt{\Delta}=\sqrt{2356}=\sqrt{4*589}=\sqrt{4}*\sqrt{589}=2\sqrt{589}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-2\sqrt{589}}{2*1}=\frac{-48-2\sqrt{589}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+2\sqrt{589}}{2*1}=\frac{-48+2\sqrt{589}}{2}
$