y-3/4y=19

Solution for y-3/4y=19 equation:

y-3/4y=19

We move all terms to the left:

y-3/4y-(19)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We multiply all the terms by the denominator


y*4y-19*4y-3=0

Wy multiply elements

4y^2-76y-3=0

a = 4; b = -76; c = -3;
Δ = b2-4ac
Δ = -762-4·4·(-3)
Δ = 5824
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:

$\sqrt{\Delta}=\sqrt{5824}=\sqrt{64*91}=\sqrt{64}*\sqrt{91}=8\sqrt{91}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-8\sqrt{91}}{2*4}=\frac{76-8\sqrt{91}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+8\sqrt{91}}{2*4}=\frac{76+8\sqrt{91}}{8}
$