y^2-7y=12=0

Solution for y^2-7y=12=0 equation:

y^2-7y=12=0

We move all terms to the left:

y^2-7y-(12)=0

a = 1; b = -7; c = -12;
Δ = b2-4ac
Δ = -72-4·1·(-12)
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{97}}{2*1}=\frac{7-\sqrt{97}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{97}}{2*1}=\frac{7+\sqrt{97}}{2}
$