10y(2-y)=7

Solution for 10y(2-y)=7 equation:

10y(2-y)=7

We move all terms to the left:

10y(2-y)-(7)=0

We add all the numbers together, and all the variables

10y(-1y+2)-7=0

We multiply parentheses

-10y^2+20y-7=0

a = -10; b = 20; c = -7;
Δ = b2-4ac
Δ = 202-4·(-10)·(-7)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{30}}{2*-10}=\frac{-20-2\sqrt{30}}{-20}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{30}}{2*-10}=\frac{-20+2\sqrt{30}}{-20}
$