(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-5)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


3x*2x+17*2x-5*2x-90*2x+1=0

Wy multiply elements

6x^2+34x-10x-180x+1=0

We add all the numbers together, and all the variables

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}
$