10x-18=10.2/4x

Solution for 10x-18=10.2/4x equation:

10x-18=10.2/4x

We move all terms to the left:

10x-18-(10.2/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

10x-(+10.2/4x)-18=0

We get rid of parentheses

10x-10.2/4x-18=0

We multiply all the terms by the denominator


10x*4x-18*4x-10.2=0

Wy multiply elements

40x^2-72x-10.2=0

a = 40; b = -72; c = -10.2;
Δ = b2-4ac
Δ = -722-4·40·(-10.2)
Δ = 6816
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:

$\sqrt{\Delta}=\sqrt{6816}=\sqrt{16*426}=\sqrt{16}*\sqrt{426}=4\sqrt{426}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{426}}{2*40}=\frac{72-4\sqrt{426}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{426}}{2*40}=\frac{72+4\sqrt{426}}{80}
$