3/4x+6=11/8x-9

Solution for 3/4x+6=11/8x-9 equation:

3/4x+6=11/8x-9

We move all terms to the left:

3/4x+6-(11/8x-9)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x-9)!=0

x∈R


We get rid of parentheses

3/4x-11/8x+9+6=0

We calculate fractions


24x/32x^2+(-44x)/32x^2+9+6=0

We add all the numbers together, and all the variables

24x/32x^2+(-44x)/32x^2+15=0

We multiply all the terms by the denominator


24x+(-44x)+15*32x^2=0

Wy multiply elements

480x^2+24x+(-44x)=0

We get rid of parentheses

480x^2+24x-44x=0

We add all the numbers together, and all the variables

480x^2-20x=0

a = 480; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·480·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*480}=\frac{0}{960}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*480}=\frac{40}{960}
=1/24
$