x2-52x-285=0

Solution for x2-52x-285=0 equation:

x2-52x-285=0

We add all the numbers together, and all the variables

x^2-52x-285=0

a = 1; b = -52; c = -285;
Δ = b2-4ac
Δ = -522-4·1·(-285)
Δ = 3844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3844}=62$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-62}{2*1}=\frac{-10}{2}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+62}{2*1}=\frac{114}{2}
=57
$