5y^2-4y=6

Solution for 5y^2-4y=6 equation:

5y^2-4y=6

We move all terms to the left:

5y^2-4y-(6)=0

a = 5; b = -4; c = -6;
Δ = b2-4ac
Δ = -42-4·5·(-6)
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{34}}{2*5}=\frac{4-2\sqrt{34}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{34}}{2*5}=\frac{4+2\sqrt{34}}{10}
$