5a^2=-12a+15

Solution for 5a^2=-12a+15 equation:

5a^2=-12a+15

We move all terms to the left:

5a^2-(-12a+15)=0

We get rid of parentheses

5a^2+12a-15=0

a = 5; b = 12; c = -15;
Δ = b2-4ac
Δ = 122-4·5·(-15)
Δ = 444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{444}=\sqrt{4*111}=\sqrt{4}*\sqrt{111}=2\sqrt{111}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{111}}{2*5}=\frac{-12-2\sqrt{111}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{111}}{2*5}=\frac{-12+2\sqrt{111}}{10}
$