X+3x+1/2x=90

Solution for X+3x+1/2x=90 equation:

X+3X+1/2X=90

We move all terms to the left:

X+3X+1/2X-(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

4X+1/2X-90=0

We multiply all the terms by the denominator


4X*2X-90*2X+1=0

Wy multiply elements

8X^2-180X+1=0

a = 8; b = -180; c = +1;
Δ = b2-4ac
Δ = -1802-4·8·1
Δ = 32368
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:

$\sqrt{\Delta}=\sqrt{32368}=\sqrt{4624*7}=\sqrt{4624}*\sqrt{7}=68\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-68\sqrt{7}}{2*8}=\frac{180-68\sqrt{7}}{16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+68\sqrt{7}}{2*8}=\frac{180+68\sqrt{7}}{16}
$