X^2+14x=374

Solution for X^2+14x=374 equation:

X^2+14X=374

We move all terms to the left:

X^2+14X-(374)=0

a = 1; b = 14; c = -374;
Δ = b2-4ac
Δ = 142-4·1·(-374)
Δ = 1692
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:

$\sqrt{\Delta}=\sqrt{1692}=\sqrt{36*47}=\sqrt{36}*\sqrt{47}=6\sqrt{47}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-6\sqrt{47}}{2*1}=\frac{-14-6\sqrt{47}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+6\sqrt{47}}{2*1}=\frac{-14+6\sqrt{47}}{2}
$