3a^2-5a=23

Solution for 3a^2-5a=23 equation:

3a^2-5a=23

We move all terms to the left:

3a^2-5a-(23)=0

a = 3; b = -5; c = -23;
Δ = b2-4ac
Δ = -52-4·3·(-23)
Δ = 301
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{-(-5)-\sqrt{301}}{2*3}=\frac{5-\sqrt{301}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{301}}{2*3}=\frac{5+\sqrt{301}}{6}
$