4x-14/7x=0

Solution for 4x-14/7x=0 equation:

4x-14/7x=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We multiply all the terms by the denominator


4x*7x-14=0

Wy multiply elements

28x^2-14=0

a = 28; b = 0; c = -14;
Δ = b2-4ac
Δ = 02-4·28·(-14)
Δ = 1568
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:

$\sqrt{\Delta}=\sqrt{1568}=\sqrt{784*2}=\sqrt{784}*\sqrt{2}=28\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28\sqrt{2}}{2*28}=\frac{0-28\sqrt{2}}{56}
=-\frac{28\sqrt{2}}{56}
=-\frac{\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28\sqrt{2}}{2*28}=\frac{0+28\sqrt{2}}{56}
=\frac{28\sqrt{2}}{56}
=\frac{\sqrt{2}}{2}
$