2a^2-3a=6

Solution for 2a^2-3a=6 equation:

2a^2-3a=6

We move all terms to the left:

2a^2-3a-(6)=0

a = 2; b = -3; c = -6;
Δ = b2-4ac
Δ = -32-4·2·(-6)
Δ = 57
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{-(-3)-\sqrt{57}}{2*2}=\frac{3-\sqrt{57}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{57}}{2*2}=\frac{3+\sqrt{57}}{4}
$