2=4a^2-3a-8

Solution for 2=4a^2-3a-8 equation:

2=4a^2-3a-8

We move all terms to the left:

2-(4a^2-3a-8)=0

We get rid of parentheses

-4a^2+3a+8+2=0

We add all the numbers together, and all the variables

-4a^2+3a+10=0

a = -4; b = 3; c = +10;
Δ = b2-4ac
Δ = 32-4·(-4)·10
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-13}{2*-4}=\frac{-16}{-8}
=+2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+13}{2*-4}=\frac{10}{-8}
=-1+1/4
$