11y=7y^2+4

Solution for 11y=7y^2+4 equation:

11y=7y^2+4

We move all terms to the left:

11y-(7y^2+4)=0

We get rid of parentheses

-7y^2+11y-4=0

a = -7; b = 11; c = -4;
Δ = b2-4ac
Δ = 112-4·(-7)·(-4)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-3}{2*-7}=\frac{-14}{-14}
=1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+3}{2*-7}=\frac{-8}{-14}
=4/7
$