74+5x(2x+8)=180

Solution for 74+5x(2x+8)=180 equation:

74+5x(2x+8)=180

We move all terms to the left:

74+5x(2x+8)-(180)=0

We add all the numbers together, and all the variables

5x(2x+8)-106=0

We multiply parentheses

10x^2+40x-106=0

a = 10; b = 40; c = -106;
Δ = b2-4ac
Δ = 402-4·10·(-106)
Δ = 5840
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:

$\sqrt{\Delta}=\sqrt{5840}=\sqrt{16*365}=\sqrt{16}*\sqrt{365}=4\sqrt{365}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{365}}{2*10}=\frac{-40-4\sqrt{365}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{365}}{2*10}=\frac{-40+4\sqrt{365}}{20}
$