(8x+1)(27x+4)=180

Solution for (8x+1)(27x+4)=180 equation:

(8x+1)(27x+4)=180

We move all terms to the left:

(8x+1)(27x+4)-(180)=0

We multiply parentheses ..

(+216x^2+32x+27x+4)-180=0

We get rid of parentheses

216x^2+32x+27x+4-180=0

We add all the numbers together, and all the variables

216x^2+59x-176=0

a = 216; b = 59; c = -176;
Δ = b2-4ac
Δ = 592-4·216·(-176)
Δ = 155545
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{-(59)-\sqrt{155545}}{2*216}=\frac{-59-\sqrt{155545}}{432}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(59)+\sqrt{155545}}{2*216}=\frac{-59+\sqrt{155545}}{432}
$