S+7/2s+10s=55

Solution for S+7/2s+10s=55 equation:

+7/2S+10S=55

We move all terms to the left:

+7/2S+10S-(55)=0


Domain of the equation: 2S!=0

S!=0/2

S!=0

S∈R


We add all the numbers together, and all the variables

10S+7/2S-55=0

We multiply all the terms by the denominator


10S*2S-55*2S+7=0

Wy multiply elements

20S^2-110S+7=0

a = 20; b = -110; c = +7;
Δ = b2-4ac
Δ = -1102-4·20·7
Δ = 11540
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:

$\sqrt{\Delta}=\sqrt{11540}=\sqrt{4*2885}=\sqrt{4}*\sqrt{2885}=2\sqrt{2885}$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-2\sqrt{2885}}{2*20}=\frac{110-2\sqrt{2885}}{40}
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+2\sqrt{2885}}{2*20}=\frac{110+2\sqrt{2885}}{40}
$