1.5=31d2/2

Solution for 1.5=31d2/2 equation:

1.5=31d^2/2

We move all terms to the left:

1.5-(31d^2/2)=0

We get rid of parentheses

-31d^2/2+1.5=0

We multiply all the terms by the denominator


-31d^2+(1.5)*2=0

We add all the numbers together, and all the variables

-31d^2+3=0

a = -31; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-31)·3
Δ = 372
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{93}}{2*-31}=\frac{0-2\sqrt{93}}{-62}
=-\frac{2\sqrt{93}}{-62}
=-\frac{\sqrt{93}}{-31}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{93}}{2*-31}=\frac{0+2\sqrt{93}}{-62}
=\frac{2\sqrt{93}}{-62}
=\frac{\sqrt{93}}{-31}
$