15x^2=27x-12

Solution for 15x^2=27x-12 equation:

15x^2=27x-12

We move all terms to the left:

15x^2-(27x-12)=0

We get rid of parentheses

15x^2-27x+12=0

a = 15; b = -27; c = +12;
Δ = b2-4ac
Δ = -272-4·15·12
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3}{2*15}=\frac{24}{30}
=4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3}{2*15}=\frac{30}{30}
=1
$