-4y+28=-3/4y+2

Solution for -4y+28=-3/4y+2 equation:

-4y+28=-3/4y+2

We move all terms to the left:

-4y+28-(-3/4y+2)=0


Domain of the equation: 4y+2)!=0

y∈R


We get rid of parentheses

-4y+3/4y-2+28=0

We multiply all the terms by the denominator


-4y*4y-2*4y+28*4y+3=0

Wy multiply elements

-16y^2-8y+112y+3=0

We add all the numbers together, and all the variables

-16y^2+104y+3=0

a = -16; b = 104; c = +3;
Δ = b2-4ac
Δ = 1042-4·(-16)·3
Δ = 11008
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:

$\sqrt{\Delta}=\sqrt{11008}=\sqrt{256*43}=\sqrt{256}*\sqrt{43}=16\sqrt{43}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(104)-16\sqrt{43}}{2*-16}=\frac{-104-16\sqrt{43}}{-32}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(104)+16\sqrt{43}}{2*-16}=\frac{-104+16\sqrt{43}}{-32}
$