10.2x=4/5x-10

Solution for 10.2x=4/5x-10 equation:

10.2x=4/5x-10

We move all terms to the left:

10.2x-(4/5x-10)=0


Domain of the equation: 5x-10)!=0

x∈R


We get rid of parentheses

10.2x-4/5x+10=0

We multiply all the terms by the denominator


(10.2x)*5x+10*5x-4=0

We add all the numbers together, and all the variables

(+10.2x)*5x+10*5x-4=0

We multiply parentheses

50x^2+10*5x-4=0

Wy multiply elements

50x^2+50x-4=0

a = 50; b = 50; c = -4;
Δ = b2-4ac
Δ = 502-4·50·(-4)
Δ = 3300
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:

$\sqrt{\Delta}=\sqrt{3300}=\sqrt{100*33}=\sqrt{100}*\sqrt{33}=10\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-10\sqrt{33}}{2*50}=\frac{-50-10\sqrt{33}}{100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+10\sqrt{33}}{2*50}=\frac{-50+10\sqrt{33}}{100}
$