8x-5=70/x

Solution for 8x-5=70/x equation:

8x-5=70/x

We move all terms to the left:

8x-5-(70/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

8x-(+70/x)-5=0

We get rid of parentheses

8x-70/x-5=0

We multiply all the terms by the denominator


8x*x-5*x-70=0

We add all the numbers together, and all the variables

-5x+8x*x-70=0

Wy multiply elements

8x^2-5x-70=0

a = 8; b = -5; c = -70;
Δ = b2-4ac
Δ = -52-4·8·(-70)
Δ = 2265
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{2265}}{2*8}=\frac{5-\sqrt{2265}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{2265}}{2*8}=\frac{5+\sqrt{2265}}{16}
$