174=(4x+5)*x

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

174=(4x+5)*x

We move all terms to the left:

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


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

(4x+5)*x

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
$