2y2+7=9y+2

Solution for 2y2+7=9y+2 equation:

2y^2+7=9y+2

We move all terms to the left:

2y^2+7-(9y+2)=0

We get rid of parentheses

2y^2-9y-2+7=0

We add all the numbers together, and all the variables

2y^2-9y+5=0

a = 2; b = -9; c = +5;
Δ = b2-4ac
Δ = -92-4·2·5
Δ = 41
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{-(-9)-\sqrt{41}}{2*2}=\frac{9-\sqrt{41}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{41}}{2*2}=\frac{9+\sqrt{41}}{4}
$