4y^2-6=y-24y^2

Solution for 4y^2-6=y-24y^2 equation:

4y^2-6=y-24y^2

We move all terms to the left:

4y^2-6-(y-24y^2)=0

We get rid of parentheses

4y^2+24y^2-y-6=0

We add all the numbers together, and all the variables

28y^2-1y-6=0

a = 28; b = -1; c = -6;
Δ = b2-4ac
Δ = -12-4·28·(-6)
Δ = 673
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{-(-1)-\sqrt{673}}{2*28}=\frac{1-\sqrt{673}}{56}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{673}}{2*28}=\frac{1+\sqrt{673}}{56}
$