(5/2)x-(1/2)=3x

Solution for (5/2)x-(1/2)=3x equation:

(5/2)x-(1/2)=3x

We move all terms to the left:

(5/2)x-(1/2)-(3x)=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+5/2)x-3x-(+1/2)=0

We add all the numbers together, and all the variables

-3x+(+5/2)x-(+1/2)=0

We multiply parentheses

5x^2-3x-(+1/2)=0

We get rid of parentheses

5x^2-3x-1/2=0

We multiply all the terms by the denominator


5x^2*2-3x*2-1=0

Wy multiply elements

10x^2-6x-1=0

a = 10; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·10·(-1)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{19}}{2*10}=\frac{6-2\sqrt{19}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{19}}{2*10}=\frac{6+2\sqrt{19}}{20}
$