174=x*(4x+5)

Solution for 174=x*(4x+5) equation:

174=x(4x+5)

We move all terms to the left:

174-(x(4x+5))=0


We calculate terms in parentheses: -(x(4x+5)), so:

x(4x+5)

We multiply parentheses

4x^2+5x

Back to the equation:

-(4x^2+5x)


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