4x-18=10/4x

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

4x-18=10/4x

We move all terms to the left:

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


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

4x-10/4x-18=0

We multiply all the terms by the denominator


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

Wy multiply elements

16x^2-72x-10=0

a = 16; b = -72; c = -10;
Δ = b2-4ac
Δ = -722-4·16·(-10)
Δ = 5824
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:

$\sqrt{\Delta}=\sqrt{5824}=\sqrt{64*91}=\sqrt{64}*\sqrt{91}=8\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-8\sqrt{91}}{2*16}=\frac{72-8\sqrt{91}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+8\sqrt{91}}{2*16}=\frac{72+8\sqrt{91}}{32}
$