42x-126/7x=14

Solution for 42x-126/7x=14 equation:

42x-126/7x=14

We move all terms to the left:

42x-126/7x-(14)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We multiply all the terms by the denominator


42x*7x-14*7x-126=0

Wy multiply elements

294x^2-98x-126=0

a = 294; b = -98; c = -126;
Δ = b2-4ac
Δ = -982-4·294·(-126)
Δ = 157780
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:

$\sqrt{\Delta}=\sqrt{157780}=\sqrt{196*805}=\sqrt{196}*\sqrt{805}=14\sqrt{805}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-98)-14\sqrt{805}}{2*294}=\frac{98-14\sqrt{805}}{588}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-98)+14\sqrt{805}}{2*294}=\frac{98+14\sqrt{805}}{588}
$