11=2/3x-1,x=15

Solution for 11=2/3x-1,x=15 equation:

11=2/3x-1.x=15

We move all terms to the left:

11-(2/3x-1.x)=0


Domain of the equation: 3x-1.x)!=0

x∈R


We add all the numbers together, and all the variables

-(-1x+2/3x)+11=0

We get rid of parentheses

1x-2/3x+11=0

We multiply all the terms by the denominator


1x*3x+11*3x-2=0

Wy multiply elements

3x^2+33x-2=0

a = 3; b = 33; c = -2;
Δ = b2-4ac
Δ = 332-4·3·(-2)
Δ = 1113
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-\sqrt{1113}}{2*3}=\frac{-33-\sqrt{1113}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+\sqrt{1113}}{2*3}=\frac{-33+\sqrt{1113}}{6}
$