X^2-14x=77

Solution for X^2-14x=77 equation:

X^2-14X=77

We move all terms to the left:

X^2-14X-(77)=0

a = 1; b = -14; c = -77;
Δ = b2-4ac
Δ = -142-4·1·(-77)
Δ = 504
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:

$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-6\sqrt{14}}{2*1}=\frac{14-6\sqrt{14}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6\sqrt{14}}{2*1}=\frac{14+6\sqrt{14}}{2}
$