2/3x+7=11x-15

Solution for 2/3x+7=11x-15 equation:

2/3x+7=11x-15

We move all terms to the left:

2/3x+7-(11x-15)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-11x+15+7=0

We multiply all the terms by the denominator


-11x*3x+15*3x+7*3x+2=0

Wy multiply elements

-33x^2+45x+21x+2=0

We add all the numbers together, and all the variables

-33x^2+66x+2=0

a = -33; b = 66; c = +2;
Δ = b2-4ac
Δ = 662-4·(-33)·2
Δ = 4620
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:

$\sqrt{\Delta}=\sqrt{4620}=\sqrt{4*1155}=\sqrt{4}*\sqrt{1155}=2\sqrt{1155}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-2\sqrt{1155}}{2*-33}=\frac{-66-2\sqrt{1155}}{-66}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+2\sqrt{1155}}{2*-33}=\frac{-66+2\sqrt{1155}}{-66}
$