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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


64x/128x^2+2x/128x^2+(-6x)/128x^2-10=0

We multiply all the terms by the denominator


64x+2x+(-6x)-10*128x^2=0

We add all the numbers together, and all the variables

66x+(-6x)-10*128x^2=0

Wy multiply elements

-1280x^2+66x+(-6x)=0

We get rid of parentheses

-1280x^2+66x-6x=0

We add all the numbers together, and all the variables

-1280x^2+60x=0

a = -1280; b = 60; c = 0;
Δ = b2-4ac
Δ = 602-4·(-1280)·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-60}{2*-1280}=\frac{-120}{-2560}
=3/64
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+60}{2*-1280}=\frac{0}{-2560}
=0
$