41/2x-3=3.7x+9

Solution for 41/2x-3=3.7x+9 equation:

41/2x-3=3.7x+9

We move all terms to the left:

41/2x-3-(3.7x+9)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

41/2x-3.7x-9-3=0

We multiply all the terms by the denominator


-(3.7x)*2x-9*2x-3*2x+41=0

We add all the numbers together, and all the variables

-(+3.7x)*2x-9*2x-3*2x+41=0

We multiply parentheses

-6x^2-9*2x-3*2x+41=0

Wy multiply elements

-6x^2-18x-6x+41=0

We add all the numbers together, and all the variables

-6x^2-24x+41=0

a = -6; b = -24; c = +41;
Δ = b2-4ac
Δ = -242-4·(-6)·41
Δ = 1560
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:

$\sqrt{\Delta}=\sqrt{1560}=\sqrt{4*390}=\sqrt{4}*\sqrt{390}=2\sqrt{390}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{390}}{2*-6}=\frac{24-2\sqrt{390}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{390}}{2*-6}=\frac{24+2\sqrt{390}}{-12}
$