6-3/4x+1/3=1/2x+15

Solution for 6-3/4x+1/3=1/2x+15 equation:

6-3/4x+1/3=1/2x+15

We move all terms to the left:

6-3/4x+1/3-(1/2x+15)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x+15)!=0

x∈R


We get rid of parentheses

-3/4x-1/2x-15+6+1/3=0

We calculate fractions


16x^2/72x^2+(-54x)/72x^2+(-36x)/72x^2-15+6=0

We add all the numbers together, and all the variables

16x^2/72x^2+(-54x)/72x^2+(-36x)/72x^2-9=0

We multiply all the terms by the denominator


16x^2+(-54x)+(-36x)-9*72x^2=0

Wy multiply elements

16x^2-648x^2+(-54x)+(-36x)=0

We get rid of parentheses

16x^2-648x^2-54x-36x=0

We add all the numbers together, and all the variables

-632x^2-90x=0

a = -632; b = -90; c = 0;
Δ = b2-4ac
Δ = -902-4·(-632)·0
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-90}{2*-632}=\frac{0}{-1264}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+90}{2*-632}=\frac{180}{-1264}
=-45/316
$