7y=3y2-4

Solution for 7y=3y2-4 equation:

7y=3y^2-4

We move all terms to the left:

7y-(3y^2-4)=0

We get rid of parentheses

-3y^2+7y+4=0

a = -3; b = 7; c = +4;
Δ = b2-4ac
Δ = 72-4·(-3)·4
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*-3}=\frac{-7-\sqrt{97}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{97}}{2*-3}=\frac{-7+\sqrt{97}}{-6}
$