X=7/3x+8

Solution for X=7/3x+8 equation:

X=7/3X+8

We move all terms to the left:

X-(7/3X+8)=0


Domain of the equation: 3X+8)!=0

X∈R


We get rid of parentheses

X-7/3X-8=0

We multiply all the terms by the denominator


X*3X-8*3X-7=0

Wy multiply elements

3X^2-24X-7=0

a = 3; b = -24; c = -7;
Δ = b2-4ac
Δ = -242-4·3·(-7)
Δ = 660
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:

$\sqrt{\Delta}=\sqrt{660}=\sqrt{4*165}=\sqrt{4}*\sqrt{165}=2\sqrt{165}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{165}}{2*3}=\frac{24-2\sqrt{165}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{165}}{2*3}=\frac{24+2\sqrt{165}}{6}
$