x(35+x)=300

Solution for x(35+x)=300 equation:

x(35+x)=300

We move all terms to the left:

x(35+x)-(300)=0

We add all the numbers together, and all the variables

x(x+35)-300=0

We multiply parentheses

x^2+35x-300=0

a = 1; b = 35; c = -300;
Δ = b2-4ac
Δ = 352-4·1·(-300)
Δ = 2425
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:

$\sqrt{\Delta}=\sqrt{2425}=\sqrt{25*97}=\sqrt{25}*\sqrt{97}=5\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-5\sqrt{97}}{2*1}=\frac{-35-5\sqrt{97}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+5\sqrt{97}}{2*1}=\frac{-35+5\sqrt{97}}{2}
$