y=-5.y^2+9y+7

Solution for y=-5.y^2+9y+7 equation:

y=-5.y^2+9y+7

We move all terms to the left:

y-(-5.y^2+9y+7)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

5.y^2-8y-7=0

a = 5.; b = -8; c = -7;
Δ = b2-4ac
Δ = -82-4·5.·(-7)
Δ = 204
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{51}}{2*5.}=\frac{8-2\sqrt{51}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{51}}{2*5.}=\frac{8+2\sqrt{51}}{10}
$