(6a-54)(5a+27)=23

Solution for (6a-54)(5a+27)=23 equation:

(6a-54)(5a+27)=23

We move all terms to the left:

(6a-54)(5a+27)-(23)=0

We multiply parentheses ..

(+30a^2+162a-270a-1458)-23=0

We get rid of parentheses

30a^2+162a-270a-1458-23=0

We add all the numbers together, and all the variables

30a^2-108a-1481=0

a = 30; b = -108; c = -1481;
Δ = b2-4ac
Δ = -1082-4·30·(-1481)
Δ = 189384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{189384}=\sqrt{4*47346}=\sqrt{4}*\sqrt{47346}=2\sqrt{47346}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-2\sqrt{47346}}{2*30}=\frac{108-2\sqrt{47346}}{60}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+2\sqrt{47346}}{2*30}=\frac{108+2\sqrt{47346}}{60}
$