(x+83)+5x(x+74)=360

Solution for (x+83)+5x(x+74)=360 equation:

(x+83)+5x(x+74)=360

We move all terms to the left:

(x+83)+5x(x+74)-(360)=0

We multiply parentheses

5x^2+(x+83)+370x-360=0

We get rid of parentheses

5x^2+x+370x+83-360=0

We add all the numbers together, and all the variables

5x^2+371x-277=0

a = 5; b = 371; c = -277;
Δ = b2-4ac
Δ = 3712-4·5·(-277)
Δ = 143181
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:

$\sqrt{\Delta}=\sqrt{143181}=\sqrt{9*15909}=\sqrt{9}*\sqrt{15909}=3\sqrt{15909}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(371)-3\sqrt{15909}}{2*5}=\frac{-371-3\sqrt{15909}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(371)+3\sqrt{15909}}{2*5}=\frac{-371+3\sqrt{15909}}{10}
$