1/2x-7=21-4x

Solution for 1/2x-7=21-4x equation:

1/2x-7=21-4x

We move all terms to the left:

1/2x-7-(21-4x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(-4x+21)-7=0

We get rid of parentheses

1/2x+4x-21-7=0

We multiply all the terms by the denominator


4x*2x-21*2x-7*2x+1=0

Wy multiply elements

8x^2-42x-14x+1=0

We add all the numbers together, and all the variables

8x^2-56x+1=0

a = 8; b = -56; c = +1;
Δ = b2-4ac
Δ = -562-4·8·1
Δ = 3104
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:

$\sqrt{\Delta}=\sqrt{3104}=\sqrt{16*194}=\sqrt{16}*\sqrt{194}=4\sqrt{194}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-4\sqrt{194}}{2*8}=\frac{56-4\sqrt{194}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+4\sqrt{194}}{2*8}=\frac{56+4\sqrt{194}}{16}
$