15x(20+x)=185

Solution for 15x(20+x)=185 equation:

15x(20+x)=185

We move all terms to the left:

15x(20+x)-(185)=0

We add all the numbers together, and all the variables

15x(x+20)-185=0

We multiply parentheses

15x^2+300x-185=0

a = 15; b = 300; c = -185;
Δ = b2-4ac
Δ = 3002-4·15·(-185)
Δ = 101100
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:

$\sqrt{\Delta}=\sqrt{101100}=\sqrt{100*1011}=\sqrt{100}*\sqrt{1011}=10\sqrt{1011}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(300)-10\sqrt{1011}}{2*15}=\frac{-300-10\sqrt{1011}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(300)+10\sqrt{1011}}{2*15}=\frac{-300+10\sqrt{1011}}{30}
$