3x+4+3/2x+25=90

Solution for 3x+4+3/2x+25=90 equation:

3x+4+3/2x+25=90

We move all terms to the left:

3x+4+3/2x+25-(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+3/2x-61=0

We multiply all the terms by the denominator


3x*2x-61*2x+3=0

Wy multiply elements

6x^2-122x+3=0

a = 6; b = -122; c = +3;
Δ = b2-4ac
Δ = -1222-4·6·3
Δ = 14812
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:

$\sqrt{\Delta}=\sqrt{14812}=\sqrt{2116*7}=\sqrt{2116}*\sqrt{7}=46\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-122)-46\sqrt{7}}{2*6}=\frac{122-46\sqrt{7}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-122)+46\sqrt{7}}{2*6}=\frac{122+46\sqrt{7}}{12}
$