12w^2=27w-15

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

12w^2=27w-15

We move all terms to the left:

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

We get rid of parentheses

12w^2-27w+15=0

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

$\sqrt{\Delta}=\sqrt{9}=3$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3}{2*12}=\frac{24}{24}
=1
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3}{2*12}=\frac{30}{24}
=1+1/4
$