167/15y+7+15y+6=180

Solution for 167/15y+7+15y+6=180 equation:

167/15y+7+15y+6=180

We move all terms to the left:

167/15y+7+15y+6-(180)=0


Domain of the equation: 15y!=0

y!=0/15

y!=0

y∈R


We add all the numbers together, and all the variables

15y+167/15y-167=0

We multiply all the terms by the denominator


15y*15y-167*15y+167=0

Wy multiply elements

225y^2-2505y+167=0

a = 225; b = -2505; c = +167;
Δ = b2-4ac
Δ = -25052-4·225·167
Δ = 6124725
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:

$\sqrt{\Delta}=\sqrt{6124725}=\sqrt{225*27221}=\sqrt{225}*\sqrt{27221}=15\sqrt{27221}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2505)-15\sqrt{27221}}{2*225}=\frac{2505-15\sqrt{27221}}{450}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2505)+15\sqrt{27221}}{2*225}=\frac{2505+15\sqrt{27221}}{450}
$