1/2x+5=14x=

Solution for 1/2x+5=14x= equation:

1/2x+5=14x=

We move all terms to the left:

1/2x+5-(14x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-14x+1/2x+5=0

We multiply all the terms by the denominator


-14x*2x+5*2x+1=0

Wy multiply elements

-28x^2+10x+1=0

a = -28; b = 10; c = +1;
Δ = b2-4ac
Δ = 102-4·(-28)·1
Δ = 212
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:

$\sqrt{\Delta}=\sqrt{212}=\sqrt{4*53}=\sqrt{4}*\sqrt{53}=2\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{53}}{2*-28}=\frac{-10-2\sqrt{53}}{-56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{53}}{2*-28}=\frac{-10+2\sqrt{53}}{-56}
$