10x-8=17+5/3x

Solution for 10x-8=17+5/3x equation:

10x-8=17+5/3x

We move all terms to the left:

10x-8-(17+5/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

10x-(5/3x+17)-8=0

We get rid of parentheses

10x-5/3x-17-8=0

We multiply all the terms by the denominator


10x*3x-17*3x-8*3x-5=0

Wy multiply elements

30x^2-51x-24x-5=0

We add all the numbers together, and all the variables

30x^2-75x-5=0

a = 30; b = -75; c = -5;
Δ = b2-4ac
Δ = -752-4·30·(-5)
Δ = 6225
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:

$\sqrt{\Delta}=\sqrt{6225}=\sqrt{25*249}=\sqrt{25}*\sqrt{249}=5\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-5\sqrt{249}}{2*30}=\frac{75-5\sqrt{249}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+5\sqrt{249}}{2*30}=\frac{75+5\sqrt{249}}{60}
$