5x-315/x=-10

Solution for 5x-315/x=-10 equation:

5x-315/x=-10

We move all terms to the left:

5x-315/x-(-10)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

5x-315/x+10=0

We multiply all the terms by the denominator


5x*x+10*x-315=0

We add all the numbers together, and all the variables

10x+5x*x-315=0

Wy multiply elements

5x^2+10x-315=0

a = 5; b = 10; c = -315;
Δ = b2-4ac
Δ = 102-4·5·(-315)
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-80}{2*5}=\frac{-90}{10}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+80}{2*5}=\frac{70}{10}
=7
$