2/5s-2+3(s-11)=125

Solution for 2/5s-2+3(s-11)=125 equation:

2/5s-2+3(s-11)=125

We move all terms to the left:

2/5s-2+3(s-11)-(125)=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+3(s-11)-127=0

We multiply parentheses

2/5s+3s-33-127=0

We multiply all the terms by the denominator


3s*5s-33*5s-127*5s+2=0

Wy multiply elements

15s^2-165s-635s+2=0

We add all the numbers together, and all the variables

15s^2-800s+2=0

a = 15; b = -800; c = +2;
Δ = b2-4ac
Δ = -8002-4·15·2
Δ = 639880
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:

$\sqrt{\Delta}=\sqrt{639880}=\sqrt{4*159970}=\sqrt{4}*\sqrt{159970}=2\sqrt{159970}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-800)-2\sqrt{159970}}{2*15}=\frac{800-2\sqrt{159970}}{30}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-800)+2\sqrt{159970}}{2*15}=\frac{800+2\sqrt{159970}}{30}
$