5s^-7/10s-9=0

Solution for 5s^-7/10s-9=0 equation:

5s^-7/10s-9=0


Domain of the equation: 10s!=0

s!=0/10

s!=0

s∈R


We add all the numbers together, and all the variables

5s-7/10s-9=0

We multiply all the terms by the denominator


5s*10s-9*10s-7=0

Wy multiply elements

50s^2-90s-7=0

a = 50; b = -90; c = -7;
Δ = b2-4ac
Δ = -902-4·50·(-7)
Δ = 9500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9500}=\sqrt{100*95}=\sqrt{100}*\sqrt{95}=10\sqrt{95}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-10\sqrt{95}}{2*50}=\frac{90-10\sqrt{95}}{100}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+10\sqrt{95}}{2*50}=\frac{90+10\sqrt{95}}{100}
$