x(x+78)=928

Solution for x(x+78)=928 equation:

x(x+78)=928

We move all terms to the left:

x(x+78)-(928)=0

We multiply parentheses

x^2+78x-928=0

a = 1; b = 78; c = -928;
Δ = b2-4ac
Δ = 782-4·1·(-928)
Δ = 9796
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:

$\sqrt{\Delta}=\sqrt{9796}=\sqrt{4*2449}=\sqrt{4}*\sqrt{2449}=2\sqrt{2449}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-2\sqrt{2449}}{2*1}=\frac{-78-2\sqrt{2449}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+2\sqrt{2449}}{2*1}=\frac{-78+2\sqrt{2449}}{2}
$