a^2-31a-282=0

Solution for a^2-31a-282=0 equation:

a^2-31a-282=0

a = 1; b = -31; c = -282;
Δ = b2-4ac
Δ = -312-4·1·(-282)
Δ = 2089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-\sqrt{2089}}{2*1}=\frac{31-\sqrt{2089}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+\sqrt{2089}}{2*1}=\frac{31+\sqrt{2089}}{2}
$