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

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

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

We move all terms to the left:

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


Domain of the equation: 2x-5)!=0

x∈R


We add all the numbers together, and all the variables

-(3x+1/2x+12)+90=0

We get rid of parentheses

-3x-1/2x-12+90=0

We multiply all the terms by the denominator


-3x*2x-12*2x+90*2x-1=0

Wy multiply elements

-6x^2-24x+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}
$