x-23=572/3x=7

Solution for x-23=572/3x=7 equation:

x-23=572/3x=7

We move all terms to the left:

x-23-(572/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+572/3x)-23=0

We get rid of parentheses

x-572/3x-23=0

We multiply all the terms by the denominator


x*3x-23*3x-572=0

Wy multiply elements

3x^2-69x-572=0

a = 3; b = -69; c = -572;
Δ = b2-4ac
Δ = -692-4·3·(-572)
Δ = 11625
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:

$\sqrt{\Delta}=\sqrt{11625}=\sqrt{25*465}=\sqrt{25}*\sqrt{465}=5\sqrt{465}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-69)-5\sqrt{465}}{2*3}=\frac{69-5\sqrt{465}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+5\sqrt{465}}{2*3}=\frac{69+5\sqrt{465}}{6}
$