(5y-4)(2y-7)=y

Solution for (5y-4)(2y-7)=y equation:

(5y-4)(2y-7)=y

We move all terms to the left:

(5y-4)(2y-7)-(y)=0

We add all the numbers together, and all the variables

-1y+(5y-4)(2y-7)=0

We multiply parentheses ..

(+10y^2-35y-8y+28)-1y=0

We get rid of parentheses

10y^2-35y-8y-1y+28=0

We add all the numbers together, and all the variables

10y^2-44y+28=0

a = 10; b = -44; c = +28;
Δ = b2-4ac
Δ = -442-4·10·28
Δ = 816
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:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{51}}{2*10}=\frac{44-4\sqrt{51}}{20}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{51}}{2*10}=\frac{44+4\sqrt{51}}{20}
$