(27x+4)(8x+1)=90

Solution for (27x+4)(8x+1)=90 equation:

(27x+4)(8x+1)=90

We move all terms to the left:

(27x+4)(8x+1)-(90)=0

We multiply parentheses ..

(+216x^2+27x+32x+4)-90=0

We get rid of parentheses

216x^2+27x+32x+4-90=0

We add all the numbers together, and all the variables

216x^2+59x-86=0

a = 216; b = 59; c = -86;
Δ = b2-4ac
Δ = 592-4·216·(-86)
Δ = 77785
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{77785}}{2*216}=\frac{-59-\sqrt{77785}}{432}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(59)+\sqrt{77785}}{2*216}=\frac{-59+\sqrt{77785}}{432}
$