x(x+3x+5)=174

Solution for x(x+3x+5)=174 equation:

x(x+3x+5)=174

We move all terms to the left:

x(x+3x+5)-(174)=0

We add all the numbers together, and all the variables

x(4x+5)-174=0

We multiply parentheses

4x^2+5x-174=0

a = 4; b = 5; c = -174;
Δ = b2-4ac
Δ = 52-4·4·(-174)
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-53}{2*4}=\frac{-58}{8}
=-7+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+53}{2*4}=\frac{48}{8}
=6
$