3+1.5x+4=4x-1/2x

Solution for 3+1.5x+4=4x-1/2x equation:

3+1.5x+4=4x-1/2x

We move all terms to the left:

3+1.5x+4-(4x-1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1.5x-(+4x-1/2x)+3+4=0

We add all the numbers together, and all the variables

1.5x-(+4x-1/2x)+7=0

We get rid of parentheses

1.5x-4x+1/2x+7=0

We multiply all the terms by the denominator


(1.5x)*2x-4x*2x+7*2x+1=0

We add all the numbers together, and all the variables

(+1.5x)*2x-4x*2x+7*2x+1=0

We multiply parentheses

2x^2-4x*2x+7*2x+1=0

Wy multiply elements

2x^2-8x^2+14x+1=0

We add all the numbers together, and all the variables

-6x^2+14x+1=0

a = -6; b = 14; c = +1;
Δ = b2-4ac
Δ = 142-4·(-6)·1
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{55}}{2*-6}=\frac{-14-2\sqrt{55}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{55}}{2*-6}=\frac{-14+2\sqrt{55}}{-12}
$