x-3/7x=112

Solution for x-3/7x=112 equation:

x-3/7x=112

We move all terms to the left:

x-3/7x-(112)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We multiply all the terms by the denominator


x*7x-112*7x-3=0

Wy multiply elements

7x^2-784x-3=0

a = 7; b = -784; c = -3;
Δ = b2-4ac
Δ = -7842-4·7·(-3)
Δ = 614740
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:

$\sqrt{\Delta}=\sqrt{614740}=\sqrt{4*153685}=\sqrt{4}*\sqrt{153685}=2\sqrt{153685}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-784)-2\sqrt{153685}}{2*7}=\frac{784-2\sqrt{153685}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-784)+2\sqrt{153685}}{2*7}=\frac{784+2\sqrt{153685}}{14}
$