1/2x+3+3x-4=90

Solution for 1/2x+3+3x-4=90 equation:

1/2x+3+3x-4=90

We move all terms to the left:

1/2x+3+3x-4-(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-91=0

We multiply all the terms by the denominator


3x*2x-91*2x+1=0

Wy multiply elements

6x^2-182x+1=0

a = 6; b = -182; c = +1;
Δ = b2-4ac
Δ = -1822-4·6·1
Δ = 33100
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:

$\sqrt{\Delta}=\sqrt{33100}=\sqrt{100*331}=\sqrt{100}*\sqrt{331}=10\sqrt{331}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-182)-10\sqrt{331}}{2*6}=\frac{182-10\sqrt{331}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-182)+10\sqrt{331}}{2*6}=\frac{182+10\sqrt{331}}{12}
$