1/2x-5=10-3/4x

Solution for 1/2x-5=10-3/4x equation:

1/2x-5=10-3/4x

We move all terms to the left:

1/2x-5-(10-3/4x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(-3/4x+10)-5=0

We get rid of parentheses

1/2x+3/4x-10-5=0

We calculate fractions


4x/8x^2+6x/8x^2-10-5=0

We add all the numbers together, and all the variables

4x/8x^2+6x/8x^2-15=0

We multiply all the terms by the denominator


4x+6x-15*8x^2=0

We add all the numbers together, and all the variables

10x-15*8x^2=0

Wy multiply elements

-120x^2+10x=0

a = -120; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-120)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-120}=\frac{-20}{-240}
=1/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-120}=\frac{0}{-240}
=0
$