13y2=32y-12

Solution for 13y2=32y-12 equation:

13y^2=32y-12

We move all terms to the left:

13y^2-(32y-12)=0

We get rid of parentheses

13y^2-32y+12=0

a = 13; b = -32; c = +12;
Δ = b2-4ac
Δ = -322-4·13·12
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-20}{2*13}=\frac{12}{26}
=6/13
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+20}{2*13}=\frac{52}{26}
=2
$