5s-7/6s=0

Solution for 5s-7/6s=0 equation:

5s-7/6s=0


Domain of the equation: 6s!=0

s!=0/6

s!=0

s∈R


We multiply all the terms by the denominator


5s*6s-7=0

Wy multiply elements

30s^2-7=0

a = 30; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·30·(-7)
Δ = 840
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:

$\sqrt{\Delta}=\sqrt{840}=\sqrt{4*210}=\sqrt{4}*\sqrt{210}=2\sqrt{210}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{210}}{2*30}=\frac{0-2\sqrt{210}}{60}
=-\frac{2\sqrt{210}}{60}
=-\frac{\sqrt{210}}{30}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{210}}{2*30}=\frac{0+2\sqrt{210}}{60}
=\frac{2\sqrt{210}}{60}
=\frac{\sqrt{210}}{30}
$