8/3x=3x+5

Solution for 8/3x=3x+5 equation:

8/3x=3x+5

We move all terms to the left:

8/3x-(3x+5)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

8/3x-3x-5=0

We multiply all the terms by the denominator


-3x*3x-5*3x+8=0

Wy multiply elements

-9x^2-15x+8=0

a = -9; b = -15; c = +8;
Δ = b2-4ac
Δ = -152-4·(-9)·8
Δ = 513
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:

$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{57}}{2*-9}=\frac{15-3\sqrt{57}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{57}}{2*-9}=\frac{15+3\sqrt{57}}{-18}
$