x(x+5)=850

Solution for x(x+5)=850 equation:

x(x+5)=850

We move all terms to the left:

x(x+5)-(850)=0

We multiply parentheses

x^2+5x-850=0

a = 1; b = 5; c = -850;
Δ = b2-4ac
Δ = 52-4·1·(-850)
Δ = 3425
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:

$\sqrt{\Delta}=\sqrt{3425}=\sqrt{25*137}=\sqrt{25}*\sqrt{137}=5\sqrt{137}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{137}}{2*1}=\frac{-5-5\sqrt{137}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{137}}{2*1}=\frac{-5+5\sqrt{137}}{2}
$