(7x+1)(18x+4)=180

Solution for (7x+1)(18x+4)=180 equation:

(7x+1)(18x+4)=180

We move all terms to the left:

(7x+1)(18x+4)-(180)=0

We multiply parentheses ..

(+126x^2+28x+18x+4)-180=0

We get rid of parentheses

126x^2+28x+18x+4-180=0

We add all the numbers together, and all the variables

126x^2+46x-176=0

a = 126; b = 46; c = -176;
Δ = b2-4ac
Δ = 462-4·126·(-176)
Δ = 90820
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{90820}=\sqrt{4*22705}=\sqrt{4}*\sqrt{22705}=2\sqrt{22705}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-2\sqrt{22705}}{2*126}=\frac{-46-2\sqrt{22705}}{252}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+2\sqrt{22705}}{2*126}=\frac{-46+2\sqrt{22705}}{252}
$