3x+17+1/2x-5=90

Solution for 3x+17+1/2x-5=90 equation:

3x+17+1/2x-5=90

We move all terms to the left:

3x+17+1/2x-5-(90)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3x+1/2x-78=0

We multiply all the terms by the denominator


3x*2x-78*2x+1=0

Wy multiply elements

6x^2-156x+1=0

a = 6; b = -156; c = +1;
Δ = b2-4ac
Δ = -1562-4·6·1
Δ = 24312
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:

$\sqrt{\Delta}=\sqrt{24312}=\sqrt{4*6078}=\sqrt{4}*\sqrt{6078}=2\sqrt{6078}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-156)-2\sqrt{6078}}{2*6}=\frac{156-2\sqrt{6078}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-156)+2\sqrt{6078}}{2*6}=\frac{156+2\sqrt{6078}}{12}
$