3/4y-y=5

Solution for 3/4y-y=5 equation:

3/4y-y=5

We move all terms to the left:

3/4y-y-(5)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We add all the numbers together, and all the variables

-1y+3/4y-5=0

We multiply all the terms by the denominator


-1y*4y-5*4y+3=0

Wy multiply elements

-4y^2-20y+3=0

a = -4; b = -20; c = +3;
Δ = b2-4ac
Δ = -202-4·(-4)·3
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-8\sqrt{7}}{2*-4}=\frac{20-8\sqrt{7}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+8\sqrt{7}}{2*-4}=\frac{20+8\sqrt{7}}{-8}
$