0.007y^2-0.03y+122=137.34

Solution for 0.007y^2-0.03y+122=137.34 equation:

0.007y^2-0.03y+122=137.34

We move all terms to the left:

0.007y^2-0.03y+122-(137.34)=0

We add all the numbers together, and all the variables

0.007y^2-0.03y-15.34=0

a = 0.007; b = -0.03; c = -15.34;
Δ = b2-4ac
Δ = -0.032-4·0.007·(-15.34)
Δ = 0.43042
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{-(-0.03)-\sqrt{0.43042}}{2*0.007}=\frac{0.03-\sqrt{0.43042}}{0.014}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.03)+\sqrt{0.43042}}{2*0.007}=\frac{0.03+\sqrt{0.43042}}{0.014}
$