3a^2-8a=51

Solution for 3a^2-8a=51 equation:

3a^2-8a=51

We move all terms to the left:

3a^2-8a-(51)=0

a = 3; b = -8; c = -51;
Δ = b2-4ac
Δ = -82-4·3·(-51)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-26}{2*3}=\frac{-18}{6}
=-3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+26}{2*3}=\frac{34}{6}
=5+2/3
$