4y^2-5y=19y

Solution for 4y^2-5y=19y equation:

4y^2-5y=19y

We move all terms to the left:

4y^2-5y-(19y)=0

We add all the numbers together, and all the variables

4y^2-24y=0

a = 4; b = -24; c = 0;
Δ = b2-4ac
Δ = -242-4·4·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24}{2*4}=\frac{0}{8}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24}{2*4}=\frac{48}{8}
=6
$