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

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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 $

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