1/4x-3=5-2x

Solution for 1/4x-3=5-2x equation:

1/4x-3=5-2x

We move all terms to the left:

1/4x-3-(5-2x)=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-(-2x+5)-3=0

We get rid of parentheses

1/4x+2x-5-3=0

We multiply all the terms by the denominator


2x*4x-5*4x-3*4x+1=0

Wy multiply elements

8x^2-20x-12x+1=0

We add all the numbers together, and all the variables

8x^2-32x+1=0

a = 8; b = -32; c = +1;
Δ = b2-4ac
Δ = -322-4·8·1
Δ = 992
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:

$\sqrt{\Delta}=\sqrt{992}=\sqrt{16*62}=\sqrt{16}*\sqrt{62}=4\sqrt{62}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{62}}{2*8}=\frac{32-4\sqrt{62}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{62}}{2*8}=\frac{32+4\sqrt{62}}{16}
$