x2-3x=524

Solution for x2-3x=524 equation:

x2-3x=524

We move all terms to the left:

x2-3x-(524)=0

We add all the numbers together, and all the variables

x^2-3x-524=0

a = 1; b = -3; c = -524;
Δ = b2-4ac
Δ = -32-4·1·(-524)
Δ = 2105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{2105}}{2*1}=\frac{3-\sqrt{2105}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{2105}}{2*1}=\frac{3+\sqrt{2105}}{2}
$