7/6x=2x-20

Solution for 7/6x=2x-20 equation:

7/6x=2x-20

We move all terms to the left:

7/6x-(2x-20)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

7/6x-2x+20=0

We multiply all the terms by the denominator


-2x*6x+20*6x+7=0

Wy multiply elements

-12x^2+120x+7=0

a = -12; b = 120; c = +7;
Δ = b2-4ac
Δ = 1202-4·(-12)·7
Δ = 14736
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:

$\sqrt{\Delta}=\sqrt{14736}=\sqrt{16*921}=\sqrt{16}*\sqrt{921}=4\sqrt{921}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-4\sqrt{921}}{2*-12}=\frac{-120-4\sqrt{921}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+4\sqrt{921}}{2*-12}=\frac{-120+4\sqrt{921}}{-24}
$