3x+4x=5/2x+9

Solution for 3x+4x=5/2x+9 equation:

3x+4x=5/2x+9

We move all terms to the left:

3x+4x-(5/2x+9)=0


Domain of the equation: 2x+9)!=0

x∈R


We add all the numbers together, and all the variables

7x-(5/2x+9)=0

We get rid of parentheses

7x-5/2x-9=0

We multiply all the terms by the denominator


7x*2x-9*2x-5=0

Wy multiply elements

14x^2-18x-5=0

a = 14; b = -18; c = -5;
Δ = b2-4ac
Δ = -182-4·14·(-5)
Δ = 604
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:

$\sqrt{\Delta}=\sqrt{604}=\sqrt{4*151}=\sqrt{4}*\sqrt{151}=2\sqrt{151}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{151}}{2*14}=\frac{18-2\sqrt{151}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{151}}{2*14}=\frac{18+2\sqrt{151}}{28}
$