3/4y+13=2y-2

Solution for 3/4y+13=2y-2 equation:

3/4y+13=2y-2

We move all terms to the left:

3/4y+13-(2y-2)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We get rid of parentheses

3/4y-2y+2+13=0

We multiply all the terms by the denominator


-2y*4y+2*4y+13*4y+3=0

Wy multiply elements

-8y^2+8y+52y+3=0

We add all the numbers together, and all the variables

-8y^2+60y+3=0

a = -8; b = 60; c = +3;
Δ = b2-4ac
Δ = 602-4·(-8)·3
Δ = 3696
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:

$\sqrt{\Delta}=\sqrt{3696}=\sqrt{16*231}=\sqrt{16}*\sqrt{231}=4\sqrt{231}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{231}}{2*-8}=\frac{-60-4\sqrt{231}}{-16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{231}}{2*-8}=\frac{-60+4\sqrt{231}}{-16}
$