X-4=8/3x+13

Solution for X-4=8/3x+13 equation:

X-4=8/3X+13

We move all terms to the left:

X-4-(8/3X+13)=0


Domain of the equation: 3X+13)!=0

X∈R


We get rid of parentheses

X-8/3X-13-4=0

We multiply all the terms by the denominator


X*3X-13*3X-4*3X-8=0

Wy multiply elements

3X^2-39X-12X-8=0

We add all the numbers together, and all the variables

3X^2-51X-8=0

a = 3; b = -51; c = -8;
Δ = b2-4ac
Δ = -512-4·3·(-8)
Δ = 2697
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-\sqrt{2697}}{2*3}=\frac{51-\sqrt{2697}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+\sqrt{2697}}{2*3}=\frac{51+\sqrt{2697}}{6}
$