2/3*x=7

Solution for 2/3*x=7 equation:

2/3*x=7

We move all terms to the left:

2/3*x-(7)=0


Domain of the equation: 3*x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-7*3*x+2=0

Wy multiply elements

-21x*x+2=0

Wy multiply elements

-21x^2+2=0

a = -21; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-21)·2
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{42}}{2*-21}=\frac{0-2\sqrt{42}}{-42}
=-\frac{2\sqrt{42}}{-42}
=-\frac{\sqrt{42}}{-21}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{42}}{2*-21}=\frac{0+2\sqrt{42}}{-42}
=\frac{2\sqrt{42}}{-42}
=\frac{\sqrt{42}}{-21}
$