8x+130-90/5x=80

Solution for 8x+130-90/5x=80 equation:

8x+130-90/5x=80

We move all terms to the left:

8x+130-90/5x-(80)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

8x-90/5x+50=0

We multiply all the terms by the denominator


8x*5x+50*5x-90=0

Wy multiply elements

40x^2+250x-90=0

a = 40; b = 250; c = -90;
Δ = b2-4ac
Δ = 2502-4·40·(-90)
Δ = 76900
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:

$\sqrt{\Delta}=\sqrt{76900}=\sqrt{100*769}=\sqrt{100}*\sqrt{769}=10\sqrt{769}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(250)-10\sqrt{769}}{2*40}=\frac{-250-10\sqrt{769}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(250)+10\sqrt{769}}{2*40}=\frac{-250+10\sqrt{769}}{80}
$