X^2+16x=74

Solution for X^2+16x=74 equation:

X^2+16X=74

We move all terms to the left:

X^2+16X-(74)=0

a = 1; b = 16; c = -74;
Δ = b2-4ac
Δ = 162-4·1·(-74)
Δ = 552
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:

$\sqrt{\Delta}=\sqrt{552}=\sqrt{4*138}=\sqrt{4}*\sqrt{138}=2\sqrt{138}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{138}}{2*1}=\frac{-16-2\sqrt{138}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{138}}{2*1}=\frac{-16+2\sqrt{138}}{2}
$