140(4)=100d2

Solution for 140(4)=100d2 equation:

140(4)=100d^2

We move all terms to the left:

140(4)-(100d^2)=0

a = -100; b = 0; c = +1404;
Δ = b2-4ac
Δ = 02-4·(-100)·1404
Δ = 561600
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:

$\sqrt{\Delta}=\sqrt{561600}=\sqrt{14400*39}=\sqrt{14400}*\sqrt{39}=120\sqrt{39}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-120\sqrt{39}}{2*-100}=\frac{0-120\sqrt{39}}{-200}
=-\frac{120\sqrt{39}}{-200}
=-\frac{3\sqrt{39}}{-5}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+120\sqrt{39}}{2*-100}=\frac{0+120\sqrt{39}}{-200}
=\frac{120\sqrt{39}}{-200}
=\frac{3\sqrt{39}}{-5}
$