3/4x+6=11/20x+9

Solution for 3/4x+6=11/20x+9 equation:

3/4x+6=11/20x+9

We move all terms to the left:

3/4x+6-(11/20x+9)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 20x+9)!=0

x∈R


We get rid of parentheses

3/4x-11/20x-9+6=0

We calculate fractions


60x/80x^2+(-44x)/80x^2-9+6=0

We add all the numbers together, and all the variables

60x/80x^2+(-44x)/80x^2-3=0

We multiply all the terms by the denominator


60x+(-44x)-3*80x^2=0

Wy multiply elements

-240x^2+60x+(-44x)=0

We get rid of parentheses

-240x^2+60x-44x=0

We add all the numbers together, and all the variables

-240x^2+16x=0

a = -240; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-240)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-240}=\frac{-32}{-480}
=1/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-240}=\frac{0}{-480}
=0
$