0.25x+1.5=2(1/2x-3)

Solution for 0.25x+1.5=2(1/2x-3) equation:

0.25x+1.5=2(1/2x-3)

We move all terms to the left:

0.25x+1.5-(2(1/2x-3))=0


Domain of the equation: 2x-3))!=0

x∈R


We multiply all the terms by the denominator


(0.25x)*2x+(1.5)*2x-3))-(2(1-3))=0

We add all the numbers together, and all the variables

(+0.25x)*2x+(1.5)*2x-3))-(2(-2))=0

We add all the numbers together, and all the variables

(+0.25x)*2x+(1.5)*2x=0

We multiply parentheses

0x^2+3x=0

We add all the numbers together, and all the variables

x^2+3x=0

a = 1; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·1·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*1}=\frac{0}{2}
=0
$