20x+x(x-15)=174

Solution for 20x+x(x-15)=174 equation:

20x+x(x-15)=174

We move all terms to the left:

20x+x(x-15)-(174)=0

We multiply parentheses

x^2+20x-15x-174=0

We add all the numbers together, and all the variables

x^2+5x-174=0

a = 1; b = 5; c = -174;
Δ = b2-4ac
Δ = 52-4·1·(-174)
Δ = 721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{721}}{2*1}=\frac{-5-\sqrt{721}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{721}}{2*1}=\frac{-5+\sqrt{721}}{2}
$