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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x-6)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


6x/8x^2+(-4x)/8x^2+6+4=0

We add all the numbers together, and all the variables

6x/8x^2+(-4x)/8x^2+10=0

We multiply all the terms by the denominator


6x+(-4x)+10*8x^2=0

Wy multiply elements

80x^2+6x+(-4x)=0

We get rid of parentheses

80x^2+6x-4x=0

We add all the numbers together, and all the variables

80x^2+2x=0

a = 80; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·80·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*80}=\frac{-4}{160}
=-1/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*80}=\frac{0}{160}
=0
$