5=2y(y-5)-5y

Solution for 5=2y(y-5)-5y equation:

5=2y(y-5)-5y

We move all terms to the left:

5-(2y(y-5)-5y)=0


We calculate terms in parentheses: -(2y(y-5)-5y), so:

2y(y-5)-5y

We add all the numbers together, and all the variables

-5y+2y(y-5)

We multiply parentheses

2y^2-5y-10y

We add all the numbers together, and all the variables

2y^2-15y

Back to the equation:

-(2y^2-15y)


We get rid of parentheses

-2y^2+15y+5=0

a = -2; b = 15; c = +5;
Δ = b2-4ac
Δ = 152-4·(-2)·5
Δ = 265
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{-(15)-\sqrt{265}}{2*-2}=\frac{-15-\sqrt{265}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{265}}{2*-2}=\frac{-15+\sqrt{265}}{-4}
$