5y+7=2y^2

Solution for 5y+7=2y^2 equation:

5y+7=2y^2

We move all terms to the left:

5y+7-(2y^2)=0

determiningTheFunctionDomain
-2y^2+5y+7=0

a = -2; b = 5; c = +7;
Δ = b2-4ac
Δ = 52-4·(-2)·7
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-9}{2*-2}=\frac{-14}{-4}
=3+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+9}{2*-2}=\frac{4}{-4}
=-1
$