z^2+14z=57

Solution for z^2+14z=57 equation:

z^2+14z=57

We move all terms to the left:

z^2+14z-(57)=0

a = 1; b = 14; c = -57;
Δ = b2-4ac
Δ = 142-4·1·(-57)
Δ = 424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{106}}{2*1}=\frac{-14-2\sqrt{106}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{106}}{2*1}=\frac{-14+2\sqrt{106}}{2}
$