2/3X-21=2x+5

Solution for 2/3X-21=2x+5 equation:

2/3X-21=2X+5

We move all terms to the left:

2/3X-21-(2X+5)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We get rid of parentheses

2/3X-2X-5-21=0

We multiply all the terms by the denominator


-2X*3X-5*3X-21*3X+2=0

Wy multiply elements

-6X^2-15X-63X+2=0

We add all the numbers together, and all the variables

-6X^2-78X+2=0

a = -6; b = -78; c = +2;
Δ = b2-4ac
Δ = -782-4·(-6)·2
Δ = 6132
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:

$\sqrt{\Delta}=\sqrt{6132}=\sqrt{4*1533}=\sqrt{4}*\sqrt{1533}=2\sqrt{1533}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{1533}}{2*-6}=\frac{78-2\sqrt{1533}}{-12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{1533}}{2*-6}=\frac{78+2\sqrt{1533}}{-12}
$