10v^2-31v+24=0

Solution for 10v^2-31v+24=0 equation:

10v^2-31v+24=0

a = 10; b = -31; c = +24;
Δ = b2-4ac
Δ = -312-4·10·24
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-1}{2*10}=\frac{30}{20}
=1+1/2
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+1}{2*10}=\frac{32}{20}
=1+3/5
$