x-34/42x=16

Solution for x-34/42x=16 equation:

x-34/42x=16

We move all terms to the left:

x-34/42x-(16)=0


Domain of the equation: 42x!=0

x!=0/42

x!=0

x∈R


We multiply all the terms by the denominator


x*42x-16*42x-34=0

Wy multiply elements

42x^2-672x-34=0

a = 42; b = -672; c = -34;
Δ = b2-4ac
Δ = -6722-4·42·(-34)
Δ = 457296
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:

$\sqrt{\Delta}=\sqrt{457296}=\sqrt{16*28581}=\sqrt{16}*\sqrt{28581}=4\sqrt{28581}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-672)-4\sqrt{28581}}{2*42}=\frac{672-4\sqrt{28581}}{84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-672)+4\sqrt{28581}}{2*42}=\frac{672+4\sqrt{28581}}{84}
$