3/4x+63/4=6-11/2x

Solution for 3/4x+63/4=6-11/2x equation:

3/4x+63/4=6-11/2x

We move all terms to the left:

3/4x+63/4-(6-11/2x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-(-11/2x+6)+63/4=0

We get rid of parentheses

3/4x+11/2x-6+63/4=0

We calculate fractions


6x/128x^2+704x/128x^2+126x/128x^2-6=0

We multiply all the terms by the denominator


6x+704x+126x-6*128x^2=0

We add all the numbers together, and all the variables

836x-6*128x^2=0

Wy multiply elements

-768x^2+836x=0

a = -768; b = 836; c = 0;
Δ = b2-4ac
Δ = 8362-4·(-768)·0
Δ = 698896
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{698896}=836$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(836)-836}{2*-768}=\frac{-1672}{-1536}
=1+17/192
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(836)+836}{2*-768}=\frac{0}{-1536}
=0
$