5a^2-23a=-12

Solution for 5a^2-23a=-12 equation:

5a^2-23a=-12

We move all terms to the left:

5a^2-23a-(-12)=0

We add all the numbers together, and all the variables

5a^2-23a+12=0

a = 5; b = -23; c = +12;
Δ = b2-4ac
Δ = -232-4·5·12
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-17}{2*5}=\frac{6}{10}
=3/5
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+17}{2*5}=\frac{40}{10}
=4
$