7y+2y2-7=3-4y

Solution for 7y+2y2-7=3-4y equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2y^2+11y-10=0

a = 2; b = 11; c = -10;
Δ = b2-4ac
Δ = 112-4·2·(-10)
Δ = 201
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{-(11)-\sqrt{201}}{2*2}=\frac{-11-\sqrt{201}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{201}}{2*2}=\frac{-11+\sqrt{201}}{4}
$