(2a+3)(a-1)=8

Solution for (2a+3)(a-1)=8 equation:

(2a+3)(a-1)=8

We move all terms to the left:

(2a+3)(a-1)-(8)=0

We multiply parentheses ..

(+2a^2-2a+3a-3)-8=0

We get rid of parentheses

2a^2-2a+3a-3-8=0

We add all the numbers together, and all the variables

2a^2+a-11=0

a = 2; b = 1; c = -11;
Δ = b2-4ac
Δ = 12-4·2·(-11)
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{89}}{2*2}=\frac{-1-\sqrt{89}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{89}}{2*2}=\frac{-1+\sqrt{89}}{4}
$