(4/3)x=53

Solution for (4/3)x=53 equation:

(4/3)x=53

We move all terms to the left:

(4/3)x-(53)=0


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+4/3)x-53=0

We multiply parentheses

4x^2-53=0

a = 4; b = 0; c = -53;
Δ = b2-4ac
Δ = 02-4·4·(-53)
Δ = 848
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:

$\sqrt{\Delta}=\sqrt{848}=\sqrt{16*53}=\sqrt{16}*\sqrt{53}=4\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{53}}{2*4}=\frac{0-4\sqrt{53}}{8}
=-\frac{4\sqrt{53}}{8}
=-\frac{\sqrt{53}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{53}}{2*4}=\frac{0+4\sqrt{53}}{8}
=\frac{4\sqrt{53}}{8}
=\frac{\sqrt{53}}{2}
$