X^2+13x-42.25=0

Solution for X^2+13x-42.25=0 equation:

X^2+13X-42.25=0

a = 1; b = 13; c = -42.25;
Δ = b2-4ac
Δ = 132-4·1·(-42.25)
Δ = 338
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:

$\sqrt{\Delta}=\sqrt{338}=\sqrt{169*2}=\sqrt{169}*\sqrt{2}=13\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13\sqrt{2}}{2*1}=\frac{-13-13\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13\sqrt{2}}{2*1}=\frac{-13+13\sqrt{2}}{2}
$