12x+10=54/10x

Solution for 12x+10=54/10x equation:

12x+10=54/10x

We move all terms to the left:

12x+10-(54/10x)=0


Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

12x-(+54/10x)+10=0

We get rid of parentheses

12x-54/10x+10=0

We multiply all the terms by the denominator


12x*10x+10*10x-54=0

Wy multiply elements

120x^2+100x-54=0

a = 120; b = 100; c = -54;
Δ = b2-4ac
Δ = 1002-4·120·(-54)
Δ = 35920
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:

$\sqrt{\Delta}=\sqrt{35920}=\sqrt{16*2245}=\sqrt{16}*\sqrt{2245}=4\sqrt{2245}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-4\sqrt{2245}}{2*120}=\frac{-100-4\sqrt{2245}}{240}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+4\sqrt{2245}}{2*120}=\frac{-100+4\sqrt{2245}}{240}
$