4x-14/7x=14

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

4x-14/7x=14

We move all terms to the left:

4x-14/7x-(14)=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*7x-14=0

Wy multiply elements

28x^2-98x-14=0

a = 28; b = -98; c = -14;
Δ = b2-4ac
Δ = -982-4·28·(-14)
Δ = 11172
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:

$\sqrt{\Delta}=\sqrt{11172}=\sqrt{196*57}=\sqrt{196}*\sqrt{57}=14\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-98)-14\sqrt{57}}{2*28}=\frac{98-14\sqrt{57}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-98)+14\sqrt{57}}{2*28}=\frac{98+14\sqrt{57}}{56}
$