1/290x+180=270x

Solution for 1/290x+180=270x equation:

1/290x+180=270x

We move all terms to the left:

1/290x+180-(270x)=0


Domain of the equation: 290x!=0

x!=0/290

x!=0

x∈R


We add all the numbers together, and all the variables

-270x+1/290x+180=0

We multiply all the terms by the denominator


-270x*290x+180*290x+1=0

Wy multiply elements

-78300x^2+52200x+1=0

a = -78300; b = 52200; c = +1;
Δ = b2-4ac
Δ = 522002-4·(-78300)·1
Δ = 2725153200
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:

$\sqrt{\Delta}=\sqrt{2725153200}=\sqrt{3600*756987}=\sqrt{3600}*\sqrt{756987}=60\sqrt{756987}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52200)-60\sqrt{756987}}{2*-78300}=\frac{-52200-60\sqrt{756987}}{-156600}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52200)+60\sqrt{756987}}{2*-78300}=\frac{-52200+60\sqrt{756987}}{-156600}
$