0.5x+2(3/4x-1)=1/4x+6

Solution for 0.5x+2(3/4x-1)=1/4x+6 equation:

0.5x+2(3/4x-1)=1/4x+6

We move all terms to the left:

0.5x+2(3/4x-1)-(1/4x+6)=0


Domain of the equation: 4x-1)!=0

x∈R



Domain of the equation: 4x+6)!=0

x∈R


We multiply parentheses

0.5x+6x-(1/4x+6)-2=0

We get rid of parentheses

0.5x+6x-1/4x-6-2=0

We multiply all the terms by the denominator


(0.5x)*4x+6x*4x-6*4x-2*4x-1=0

We add all the numbers together, and all the variables

(+0.5x)*4x+6x*4x-6*4x-2*4x-1=0

We multiply parentheses

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

Wy multiply elements

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

We add all the numbers together, and all the variables

25x^2-32x-1=0

a = 25; b = -32; c = -1;
Δ = b2-4ac
Δ = -322-4·25·(-1)
Δ = 1124
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:

$\sqrt{\Delta}=\sqrt{1124}=\sqrt{4*281}=\sqrt{4}*\sqrt{281}=2\sqrt{281}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{281}}{2*25}=\frac{32-2\sqrt{281}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{281}}{2*25}=\frac{32+2\sqrt{281}}{50}
$