6-3/5x+1/3=1/2x+5

Solution for 6-3/5x+1/3=1/2x+5 equation:

6-3/5x+1/3=1/2x+5

We move all terms to the left:

6-3/5x+1/3-(1/2x+5)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x+5)!=0

x∈R


We get rid of parentheses

-3/5x-1/2x-5+6+1/3=0

We calculate fractions


20x^2/90x^2+(-54x)/90x^2+(-45x)/90x^2-5+6=0

We add all the numbers together, and all the variables

20x^2/90x^2+(-54x)/90x^2+(-45x)/90x^2+1=0

We multiply all the terms by the denominator


20x^2+(-54x)+(-45x)+1*90x^2=0

Wy multiply elements

20x^2+90x^2+(-54x)+(-45x)=0

We get rid of parentheses

20x^2+90x^2-54x-45x=0

We add all the numbers together, and all the variables

110x^2-99x=0

a = 110; b = -99; c = 0;
Δ = b2-4ac
Δ = -992-4·110·0
Δ = 9801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9801}=99$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-99)-99}{2*110}=\frac{0}{220}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+99}{2*110}=\frac{198}{220}
=9/10
$