74+x(2x-7)=180

Solution for 74+x(2x-7)=180 equation:

74+x(2x-7)=180

We move all terms to the left:

74+x(2x-7)-(180)=0

We add all the numbers together, and all the variables

x(2x-7)-106=0

We multiply parentheses

2x^2-7x-106=0

a = 2; b = -7; c = -106;
Δ = b2-4ac
Δ = -72-4·2·(-106)
Δ = 897
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{897}}{2*2}=\frac{7-\sqrt{897}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{897}}{2*2}=\frac{7+\sqrt{897}}{4}
$