7.5s^2-1.5s-10.5=0

Solution for 7.5s^2-1.5s-10.5=0 equation:

7.5s^2-1.5s-10.5=0

a = 7.5; b = -1.5; c = -10.5;
Δ = b2-4ac
Δ = -1.52-4·7.5·(-10.5)
Δ = 317.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1.5)-\sqrt{317.25}}{2*7.5}=\frac{1.5-\sqrt{317.25}}{15}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.5)+\sqrt{317.25}}{2*7.5}=\frac{1.5+\sqrt{317.25}}{15}
$