3x-20=70/6x

Solution for 3x-20=70/6x equation:

3x-20=70/6x

We move all terms to the left:

3x-20-(70/6x)=0


Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(+70/6x)-20=0

We get rid of parentheses

3x-70/6x-20=0

We multiply all the terms by the denominator


3x*6x-20*6x-70=0

Wy multiply elements

18x^2-120x-70=0

a = 18; b = -120; c = -70;
Δ = b2-4ac
Δ = -1202-4·18·(-70)
Δ = 19440
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:

$\sqrt{\Delta}=\sqrt{19440}=\sqrt{1296*15}=\sqrt{1296}*\sqrt{15}=36\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-36\sqrt{15}}{2*18}=\frac{120-36\sqrt{15}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+36\sqrt{15}}{2*18}=\frac{120+36\sqrt{15}}{36}
$