3/4y-4=2y+3

Solution for 3/4y-4=2y+3 equation:

3/4y-4=2y+3

We move all terms to the left:

3/4y-4-(2y+3)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We get rid of parentheses

3/4y-2y-3-4=0

We multiply all the terms by the denominator


-2y*4y-3*4y-4*4y+3=0

Wy multiply elements

-8y^2-12y-16y+3=0

We add all the numbers together, and all the variables

-8y^2-28y+3=0

a = -8; b = -28; c = +3;
Δ = b2-4ac
Δ = -282-4·(-8)·3
Δ = 880
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:

$\sqrt{\Delta}=\sqrt{880}=\sqrt{16*55}=\sqrt{16}*\sqrt{55}=4\sqrt{55}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{55}}{2*-8}=\frac{28-4\sqrt{55}}{-16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{55}}{2*-8}=\frac{28+4\sqrt{55}}{-16}
$