6a^2=9a+15

Solution for 6a^2=9a+15 equation:

6a^2=9a+15

We move all terms to the left:

6a^2-(9a+15)=0

We get rid of parentheses

6a^2-9a-15=0

a = 6; b = -9; c = -15;
Δ = b2-4ac
Δ = -92-4·6·(-15)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-21}{2*6}=\frac{-12}{12}
=-1
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+21}{2*6}=\frac{30}{12}
=2+1/2
$