8.1x-2.1x+20=10/5x-4

Solution for 8.1x-2.1x+20=10/5x-4 equation:

8.1x-2.1x+20=10/5x-4

We move all terms to the left:

8.1x-2.1x+20-(10/5x-4)=0


Domain of the equation: 5x-4)!=0

x∈R


We add all the numbers together, and all the variables

6x-(10/5x-4)+20=0

We get rid of parentheses

6x-10/5x+4+20=0

We multiply all the terms by the denominator


6x*5x+4*5x+20*5x-10=0

Wy multiply elements

30x^2+20x+100x-10=0

We add all the numbers together, and all the variables

30x^2+120x-10=0

a = 30; b = 120; c = -10;
Δ = b2-4ac
Δ = 1202-4·30·(-10)
Δ = 15600
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:

$\sqrt{\Delta}=\sqrt{15600}=\sqrt{400*39}=\sqrt{400}*\sqrt{39}=20\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-20\sqrt{39}}{2*30}=\frac{-120-20\sqrt{39}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+20\sqrt{39}}{2*30}=\frac{-120+20\sqrt{39}}{60}
$