3/4x-5=1/2x+6

Solution for 3/4x-5=1/2x+6 equation:

3/4x-5=1/2x+6

We move all terms to the left:

3/4x-5-(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-6-5=0

We calculate fractions


6x/8x^2+(-4x)/8x^2-6-5=0

We add all the numbers together, and all the variables

6x/8x^2+(-4x)/8x^2-11=0

We multiply all the terms by the denominator


6x+(-4x)-11*8x^2=0

Wy multiply elements

-88x^2+6x+(-4x)=0

We get rid of parentheses

-88x^2+6x-4x=0

We add all the numbers together, and all the variables

-88x^2+2x=0

a = -88; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-88)·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*-88}=\frac{-4}{-176}
=1/44
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-88}=\frac{0}{-176}
=0
$