x(x+14)=94

Solution for x(x+14)=94 equation:

x(x+14)=94

We move all terms to the left:

x(x+14)-(94)=0

We multiply parentheses

x^2+14x-94=0

a = 1; b = 14; c = -94;
Δ = b2-4ac
Δ = 142-4·1·(-94)
Δ = 572
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:

$\sqrt{\Delta}=\sqrt{572}=\sqrt{4*143}=\sqrt{4}*\sqrt{143}=2\sqrt{143}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{143}}{2*1}=\frac{-14-2\sqrt{143}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{143}}{2*1}=\frac{-14+2\sqrt{143}}{2}
$