1/4x-3(x-2)=-2.25x+1

Solution for 1/4x-3(x-2)=-2.25x+1 equation:

1/4x-3(x-2)=-2.25x+1

We move all terms to the left:

1/4x-3(x-2)-(-2.25x+1)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply parentheses

1/4x-3x-(-2.25x+1)+6=0

We get rid of parentheses

1/4x-3x+2.25x-1+6=0

We multiply all the terms by the denominator


-3x*4x+(2.25x)*4x-1*4x+6*4x+1=0

We add all the numbers together, and all the variables

-3x*4x+(+2.25x)*4x-1*4x+6*4x+1=0

We multiply parentheses

8x^2-3x*4x-1*4x+6*4x+1=0

Wy multiply elements

8x^2-12x^2-4x+24x+1=0

We add all the numbers together, and all the variables

-4x^2+20x+1=0

a = -4; b = 20; c = +1;
Δ = b2-4ac
Δ = 202-4·(-4)·1
Δ = 416
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:

$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{26}}{2*-4}=\frac{-20-4\sqrt{26}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{26}}{2*-4}=\frac{-20+4\sqrt{26}}{-8}
$