23y+7y^2=20

Solution for 23y+7y^2=20 equation:

23y+7y^2=20

We move all terms to the left:

23y+7y^2-(20)=0

a = 7; b = 23; c = -20;
Δ = b2-4ac
Δ = 232-4·7·(-20)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-33}{2*7}=\frac{-56}{14}
=-4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+33}{2*7}=\frac{10}{14}
=5/7
$