X^2=13x+40=0

Solution for X^2=13x+40=0 equation:

X^2=13X+40=0

We move all terms to the left:

X^2-(13X+40)=0

We get rid of parentheses

X^2-13X-40=0

a = 1; b = -13; c = -40;
Δ = b2-4ac
Δ = -132-4·1·(-40)
Δ = 329
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{-(-13)-\sqrt{329}}{2*1}=\frac{13-\sqrt{329}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{329}}{2*1}=\frac{13+\sqrt{329}}{2}
$