x=1/42x-16

Solution for x=1/42x-16 equation:

x=1/42x-16

We move all terms to the left:

x-(1/42x-16)=0


Domain of the equation: 42x-16)!=0

x∈R


We get rid of parentheses

x-1/42x+16=0

We multiply all the terms by the denominator


x*42x+16*42x-1=0

Wy multiply elements

42x^2+672x-1=0

a = 42; b = 672; c = -1;
Δ = b2-4ac
Δ = 6722-4·42·(-1)
Δ = 451752
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:

$\sqrt{\Delta}=\sqrt{451752}=\sqrt{4*112938}=\sqrt{4}*\sqrt{112938}=2\sqrt{112938}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(672)-2\sqrt{112938}}{2*42}=\frac{-672-2\sqrt{112938}}{84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(672)+2\sqrt{112938}}{2*42}=\frac{-672+2\sqrt{112938}}{84}
$