1/4x-2=3-0.75x

Solution for 1/4x-2=3-0.75x equation:

1/4x-2=3-0.75x

We move all terms to the left:

1/4x-2-(3-0.75x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

1/4x-(-0.75x+3)-2=0

We get rid of parentheses

1/4x+0.75x-3-2=0

We multiply all the terms by the denominator


(0.75x)*4x-3*4x-2*4x+1=0

We add all the numbers together, and all the variables

(+0.75x)*4x-3*4x-2*4x+1=0

We multiply parentheses

0x^2-3*4x-2*4x+1=0

Wy multiply elements

0x^2-12x-8x+1=0

We add all the numbers together, and all the variables

x^2-20x+1=0

a = 1; b = -20; c = +1;
Δ = b2-4ac
Δ = -202-4·1·1
Δ = 396
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:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-6\sqrt{11}}{2*1}=\frac{20-6\sqrt{11}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+6\sqrt{11}}{2*1}=\frac{20+6\sqrt{11}}{2}
$