3/8x+50=x+31

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

3/8x+50=x+31

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We get rid of parentheses

3/8x-x-31+50=0

We multiply all the terms by the denominator


-x*8x-31*8x+50*8x+3=0

Wy multiply elements

-8x^2-248x+400x+3=0

We add all the numbers together, and all the variables

-8x^2+152x+3=0

a = -8; b = 152; c = +3;
Δ = b2-4ac
Δ = 1522-4·(-8)·3
Δ = 23200
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:

$\sqrt{\Delta}=\sqrt{23200}=\sqrt{400*58}=\sqrt{400}*\sqrt{58}=20\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(152)-20\sqrt{58}}{2*-8}=\frac{-152-20\sqrt{58}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(152)+20\sqrt{58}}{2*-8}=\frac{-152+20\sqrt{58}}{-16}
$