3/4y+9=-2y-2

Solution for 3/4y+9=-2y-2 equation:

3/4y+9=-2y-2

We move all terms to the left:

3/4y+9-(-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+9=0

We multiply all the terms by the denominator


2y*4y+2*4y+9*4y+3=0

Wy multiply elements

8y^2+8y+36y+3=0

We add all the numbers together, and all the variables

8y^2+44y+3=0

a = 8; b = 44; c = +3;
Δ = b2-4ac
Δ = 442-4·8·3
Δ = 1840
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:

$\sqrt{\Delta}=\sqrt{1840}=\sqrt{16*115}=\sqrt{16}*\sqrt{115}=4\sqrt{115}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{115}}{2*8}=\frac{-44-4\sqrt{115}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{115}}{2*8}=\frac{-44+4\sqrt{115}}{16}
$