4x=1/2x-14

Solution for 4x=1/2x-14 equation:

4x=1/2x-14

We move all terms to the left:

4x-(1/2x-14)=0


Domain of the equation: 2x-14)!=0

x∈R


We get rid of parentheses

4x-1/2x+14=0

We multiply all the terms by the denominator


4x*2x+14*2x-1=0

Wy multiply elements

8x^2+28x-1=0

a = 8; b = 28; c = -1;
Δ = b2-4ac
Δ = 282-4·8·(-1)
Δ = 816
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:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{51}}{2*8}=\frac{-28-4\sqrt{51}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{51}}{2*8}=\frac{-28+4\sqrt{51}}{16}
$