s+2/12s+10=45

Solution for s+2/12s+10=45 equation:

s+2/12s+10=45

We move all terms to the left:

s+2/12s+10-(45)=0


Domain of the equation: 12s!=0

s!=0/12

s!=0

s∈R


We add all the numbers together, and all the variables

s+2/12s-35=0

We multiply all the terms by the denominator


s*12s-35*12s+2=0

Wy multiply elements

12s^2-420s+2=0

a = 12; b = -420; c = +2;
Δ = b2-4ac
Δ = -4202-4·12·2
Δ = 176304
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:

$\sqrt{\Delta}=\sqrt{176304}=\sqrt{16*11019}=\sqrt{16}*\sqrt{11019}=4\sqrt{11019}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-420)-4\sqrt{11019}}{2*12}=\frac{420-4\sqrt{11019}}{24}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-420)+4\sqrt{11019}}{2*12}=\frac{420+4\sqrt{11019}}{24}
$