X^2=14x+60

Solution for X^2=14x+60 equation:

X^2=14X+60

We move all terms to the left:

X^2-(14X+60)=0

We get rid of parentheses

X^2-14X-60=0

a = 1; b = -14; c = -60;
Δ = b2-4ac
Δ = -142-4·1·(-60)
Δ = 436
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:

$\sqrt{\Delta}=\sqrt{436}=\sqrt{4*109}=\sqrt{4}*\sqrt{109}=2\sqrt{109}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{109}}{2*1}=\frac{14-2\sqrt{109}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{109}}{2*1}=\frac{14+2\sqrt{109}}{2}
$