0.5x-1.75=1/3x+1

Solution for 0.5x-1.75=1/3x+1 equation:

0.5x-1.75=1/3x+1

We move all terms to the left:

0.5x-1.75-(1/3x+1)=0


Domain of the equation: 3x+1)!=0

x∈R


We get rid of parentheses

0.5x-1/3x-1-1.75=0

We multiply all the terms by the denominator


(0.5x)*3x-1*3x-(1.75)*3x-1=0

We add all the numbers together, and all the variables

(+0.5x)*3x-1*3x-(1.75)*3x-1=0

We multiply parentheses

0x^2-1*3x-5.25x-1=0

Wy multiply elements

0x^2-3x-5.25x-1=0

We add all the numbers together, and all the variables

x^2-8.25x-1=0

a = 1; b = -8.25; c = -1;
Δ = b2-4ac
Δ = -8.252-4·1·(-1)
Δ = 72.0625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8.25)-\sqrt{72.0625}}{2*1}=\frac{8.25-\sqrt{72.0625}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8.25)+\sqrt{72.0625}}{2*1}=\frac{8.25+\sqrt{72.0625}}{2}
$