X^2=17x+56

Solution for X^2=17x+56 equation:

X^2=17X+56

We move all terms to the left:

X^2-(17X+56)=0

We get rid of parentheses

X^2-17X-56=0

a = 1; b = -17; c = -56;
Δ = b2-4ac
Δ = -172-4·1·(-56)
Δ = 513
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:

$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-3\sqrt{57}}{2*1}=\frac{17-3\sqrt{57}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+3\sqrt{57}}{2*1}=\frac{17+3\sqrt{57}}{2}
$