6y^2=42y-72

Solution for 6y^2=42y-72 equation:

6y^2=42y-72

We move all terms to the left:

6y^2-(42y-72)=0

We get rid of parentheses

6y^2-42y+72=0

a = 6; b = -42; c = +72;
Δ = b2-4ac
Δ = -422-4·6·72
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-6}{2*6}=\frac{36}{12}
=3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+6}{2*6}=\frac{48}{12}
=4
$