3-3/5x=1/2x+7

Solution for 3-3/5x=1/2x+7 equation:

3-3/5x=1/2x+7

We move all terms to the left:

3-3/5x-(1/2x+7)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x+7)!=0

x∈R


We get rid of parentheses

-3/5x-1/2x-7+3=0

We calculate fractions


(-6x)/10x^2+(-5x)/10x^2-7+3=0

We add all the numbers together, and all the variables

(-6x)/10x^2+(-5x)/10x^2-4=0

We multiply all the terms by the denominator


(-6x)+(-5x)-4*10x^2=0

Wy multiply elements

-40x^2+(-6x)+(-5x)=0

We get rid of parentheses

-40x^2-6x-5x=0

We add all the numbers together, and all the variables

-40x^2-11x=0

a = -40; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·(-40)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*-40}=\frac{0}{-80}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*-40}=\frac{22}{-80}
=-11/40
$