3/8x+50+31+x=180

Solution for 3/8x+50+31+x=180 equation:

3/8x+50+31+x=180

We move all terms to the left:

3/8x+50+31+x-(180)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

x+3/8x-99=0

We multiply all the terms by the denominator


x*8x-99*8x+3=0

Wy multiply elements

8x^2-792x+3=0

a = 8; b = -792; c = +3;
Δ = b2-4ac
Δ = -7922-4·8·3
Δ = 627168
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{627168}=\sqrt{16*39198}=\sqrt{16}*\sqrt{39198}=4\sqrt{39198}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-792)-4\sqrt{39198}}{2*8}=\frac{792-4\sqrt{39198}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-792)+4\sqrt{39198}}{2*8}=\frac{792+4\sqrt{39198}}{16}
$