1/2x+3=3/4x-13

Solution for 1/2x+3=3/4x-13 equation:

1/2x+3=3/4x-13

We move all terms to the left:

1/2x+3-(3/4x-13)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x-13)!=0

x∈R


We get rid of parentheses

1/2x-3/4x+13+3=0

We calculate fractions


4x/8x^2+(-6x)/8x^2+13+3=0

We add all the numbers together, and all the variables

4x/8x^2+(-6x)/8x^2+16=0

We multiply all the terms by the denominator


4x+(-6x)+16*8x^2=0

Wy multiply elements

128x^2+4x+(-6x)=0

We get rid of parentheses

128x^2+4x-6x=0

We add all the numbers together, and all the variables

128x^2-2x=0

a = 128; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·128·0
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*128}=\frac{0}{256}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*128}=\frac{4}{256}
=1/64
$