3/2y+8+90+y+32=180

Solution for 3/2y+8+90+y+32=180 equation:

3/2y+8+90+y+32=180

We move all terms to the left:

3/2y+8+90+y+32-(180)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

y+3/2y-50=0

We multiply all the terms by the denominator


y*2y-50*2y+3=0

Wy multiply elements

2y^2-100y+3=0

a = 2; b = -100; c = +3;
Δ = b2-4ac
Δ = -1002-4·2·3
Δ = 9976
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:

$\sqrt{\Delta}=\sqrt{9976}=\sqrt{4*2494}=\sqrt{4}*\sqrt{2494}=2\sqrt{2494}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-2\sqrt{2494}}{2*2}=\frac{100-2\sqrt{2494}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+2\sqrt{2494}}{2*2}=\frac{100+2\sqrt{2494}}{4}
$