2/5s-2+3(5-11)=50s=1/175

Solution for 2/5s-2+3(5-11)=50s=1/175 equation:

2/5s-2+3(5-11)=50s=1/175

We move all terms to the left:

2/5s-2+3(5-11)-(50s)=0


Domain of the equation: 5s!=0

s!=0/5

s!=0

s∈R


We add all the numbers together, and all the variables

2/5s-50s-2+3(-6)=0

We add all the numbers together, and all the variables

-50s+2/5s-20=0

We multiply all the terms by the denominator


-50s*5s-20*5s+2=0

Wy multiply elements

-250s^2-100s+2=0

a = -250; b = -100; c = +2;
Δ = b2-4ac
Δ = -1002-4·(-250)·2
Δ = 12000
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:

$\sqrt{\Delta}=\sqrt{12000}=\sqrt{400*30}=\sqrt{400}*\sqrt{30}=20\sqrt{30}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-20\sqrt{30}}{2*-250}=\frac{100-20\sqrt{30}}{-500}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+20\sqrt{30}}{2*-250}=\frac{100+20\sqrt{30}}{-500}
$