20-6x=2/5x-44

Solution for 20-6x=2/5x-44 equation:

20-6x=2/5x-44

We move all terms to the left:

20-6x-(2/5x-44)=0


Domain of the equation: 5x-44)!=0

x∈R


We get rid of parentheses

-6x-2/5x+44+20=0

We multiply all the terms by the denominator


-6x*5x+44*5x+20*5x-2=0

Wy multiply elements

-30x^2+220x+100x-2=0

We add all the numbers together, and all the variables

-30x^2+320x-2=0

a = -30; b = 320; c = -2;
Δ = b2-4ac
Δ = 3202-4·(-30)·(-2)
Δ = 102160
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:

$\sqrt{\Delta}=\sqrt{102160}=\sqrt{16*6385}=\sqrt{16}*\sqrt{6385}=4\sqrt{6385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(320)-4\sqrt{6385}}{2*-30}=\frac{-320-4\sqrt{6385}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(320)+4\sqrt{6385}}{2*-30}=\frac{-320+4\sqrt{6385}}{-60}
$