3/4x-1/2x=35

Solution for 3/4x-1/2x=35 equation:

3/4x-1/2x=35

We move all terms to the left:

3/4x-1/2x-(35)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


6x/8x^2+(-4x)/8x^2-35=0

We multiply all the terms by the denominator


6x+(-4x)-35*8x^2=0

Wy multiply elements

-280x^2+6x+(-4x)=0

We get rid of parentheses

-280x^2+6x-4x=0

We add all the numbers together, and all the variables

-280x^2+2x=0

a = -280; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-280)·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*-280}=\frac{-4}{-560}
=1/140
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-280}=\frac{0}{-560}
=0
$