3x-5/x=70

Solution for 3x-5/x=70 equation:

3x-5/x=70

We move all terms to the left:

3x-5/x-(70)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


3x*x-70*x-5=0

We add all the numbers together, and all the variables

-70x+3x*x-5=0

Wy multiply elements

3x^2-70x-5=0

a = 3; b = -70; c = -5;
Δ = b2-4ac
Δ = -702-4·3·(-5)
Δ = 4960
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:

$\sqrt{\Delta}=\sqrt{4960}=\sqrt{16*310}=\sqrt{16}*\sqrt{310}=4\sqrt{310}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-4\sqrt{310}}{2*3}=\frac{70-4\sqrt{310}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+4\sqrt{310}}{2*3}=\frac{70+4\sqrt{310}}{6}
$