3/5x+1/2x-4=7

Solution for 3/5x+1/2x-4=7 equation:

3/5x+1/2x-4=7

We move all terms to the left:

3/5x+1/2x-4-(7)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3/5x+1/2x-11=0

We calculate fractions


6x/10x^2+5x/10x^2-11=0

We multiply all the terms by the denominator


6x+5x-11*10x^2=0

We add all the numbers together, and all the variables

11x-11*10x^2=0

Wy multiply elements

-110x^2+11x=0

a = -110; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-110)·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*-110}=\frac{-22}{-220}
=1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-110}=\frac{0}{-220}
=0
$