4y(y-3)=6y-7

Solution for 4y(y-3)=6y-7 equation:

4y(y-3)=6y-7

We move all terms to the left:

4y(y-3)-(6y-7)=0

We multiply parentheses

4y^2-12y-(6y-7)=0

We get rid of parentheses

4y^2-12y-6y+7=0

We add all the numbers together, and all the variables

4y^2-18y+7=0

a = 4; b = -18; c = +7;
Δ = b2-4ac
Δ = -182-4·4·7
Δ = 212
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:

$\sqrt{\Delta}=\sqrt{212}=\sqrt{4*53}=\sqrt{4}*\sqrt{53}=2\sqrt{53}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{53}}{2*4}=\frac{18-2\sqrt{53}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{53}}{2*4}=\frac{18+2\sqrt{53}}{8}
$