168/x=2x-10

Solution for 168/x=2x-10 equation:

168/x=2x-10

We move all terms to the left:

168/x-(2x-10)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

168/x-2x+10=0

We multiply all the terms by the denominator


-2x*x+10*x+168=0

We add all the numbers together, and all the variables

10x-2x*x+168=0

Wy multiply elements

-2x^2+10x+168=0

a = -2; b = 10; c = +168;
Δ = b2-4ac
Δ = 102-4·(-2)·168
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-38}{2*-2}=\frac{-48}{-4}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+38}{2*-2}=\frac{28}{-4}
=-7
$