8/9x+20=11x

Solution for 8/9x+20=11x equation:

8/9x+20=11x

We move all terms to the left:

8/9x+20-(11x)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

-11x+8/9x+20=0

We multiply all the terms by the denominator


-11x*9x+20*9x+8=0

Wy multiply elements

-99x^2+180x+8=0

a = -99; b = 180; c = +8;
Δ = b2-4ac
Δ = 1802-4·(-99)·8
Δ = 35568
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{35568}=\sqrt{144*247}=\sqrt{144}*\sqrt{247}=12\sqrt{247}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-12\sqrt{247}}{2*-99}=\frac{-180-12\sqrt{247}}{-198}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+12\sqrt{247}}{2*-99}=\frac{-180+12\sqrt{247}}{-198}
$