2/3*x=52

Solution for 2/3*x=52 equation:

2/3*x=52

We move all terms to the left:

2/3*x-(52)=0


Domain of the equation: 3*x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-52*3*x+2=0

Wy multiply elements

-156x*x+2=0

Wy multiply elements

-156x^2+2=0

a = -156; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-156)·2
Δ = 1248
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:

$\sqrt{\Delta}=\sqrt{1248}=\sqrt{16*78}=\sqrt{16}*\sqrt{78}=4\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{78}}{2*-156}=\frac{0-4\sqrt{78}}{-312}
=-\frac{4\sqrt{78}}{-312}
=-\frac{\sqrt{78}}{-78}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{78}}{2*-156}=\frac{0+4\sqrt{78}}{-312}
=\frac{4\sqrt{78}}{-312}
=\frac{\sqrt{78}}{-78}
$