3x+10=5/2x+18

Solution for 3x+10=5/2x+18 equation:

3x+10=5/2x+18

We move all terms to the left:

3x+10-(5/2x+18)=0


Domain of the equation: 2x+18)!=0

x∈R


We get rid of parentheses

3x-5/2x-18+10=0

We multiply all the terms by the denominator


3x*2x-18*2x+10*2x-5=0

Wy multiply elements

6x^2-36x+20x-5=0

We add all the numbers together, and all the variables

6x^2-16x-5=0

a = 6; b = -16; c = -5;
Δ = b2-4ac
Δ = -162-4·6·(-5)
Δ = 376
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:

$\sqrt{\Delta}=\sqrt{376}=\sqrt{4*94}=\sqrt{4}*\sqrt{94}=2\sqrt{94}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{94}}{2*6}=\frac{16-2\sqrt{94}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{94}}{2*6}=\frac{16+2\sqrt{94}}{12}
$