x^2-15x=2800

Solution for x^2-15x=2800 equation:

x^2-15x=2800

We move all terms to the left:

x^2-15x-(2800)=0

a = 1; b = -15; c = -2800;
Δ = b2-4ac
Δ = -152-4·1·(-2800)
Δ = 11425
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:

$\sqrt{\Delta}=\sqrt{11425}=\sqrt{25*457}=\sqrt{25}*\sqrt{457}=5\sqrt{457}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-5\sqrt{457}}{2*1}=\frac{15-5\sqrt{457}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5\sqrt{457}}{2*1}=\frac{15+5\sqrt{457}}{2}
$