X^2=17x+40

Solution for X^2=17x+40 equation:

X^2=17X+40

We move all terms to the left:

X^2-(17X+40)=0

We get rid of parentheses

X^2-17X-40=0

a = 1; b = -17; c = -40;
Δ = b2-4ac
Δ = -172-4·1·(-40)
Δ = 449
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{-(-17)-\sqrt{449}}{2*1}=\frac{17-\sqrt{449}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{449}}{2*1}=\frac{17+\sqrt{449}}{2}
$