x(2x+7)+4=180

Solution for x(2x+7)+4=180 equation:

x(2x+7)+4=180

We move all terms to the left:

x(2x+7)+4-(180)=0

We add all the numbers together, and all the variables

x(2x+7)-176=0

We multiply parentheses

2x^2+7x-176=0

a = 2; b = 7; c = -176;
Δ = b2-4ac
Δ = 72-4·2·(-176)
Δ = 1457
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{1457}}{2*2}=\frac{-7-\sqrt{1457}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{1457}}{2*2}=\frac{-7+\sqrt{1457}}{4}
$