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

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

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

We move all terms to the left:

6-1/2x-(3/4x+1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x+1)!=0

x∈R


We get rid of parentheses

-1/2x-3/4x-1+6=0

We calculate fractions


(-4x)/8x^2+(-6x)/8x^2-1+6=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

40x^2+(-4x)+(-6x)=0

We get rid of parentheses

40x^2-4x-6x=0

We add all the numbers together, and all the variables

40x^2-10x=0

a = 40; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·40·0
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*40}=\frac{0}{80}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*40}=\frac{20}{80}
=1/4
$