420/d=30d=

Solution for 420/d=30d= equation:

420/d=30d=

We move all terms to the left:

420/d-(30d)=0


Domain of the equation: d!=0

d∈R


We add all the numbers together, and all the variables

-30d+420/d=0

We multiply all the terms by the denominator


-30d*d+420=0

Wy multiply elements

-30d^2+420=0

a = -30; b = 0; c = +420;
Δ = b2-4ac
Δ = 02-4·(-30)·420
Δ = 50400
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:

$\sqrt{\Delta}=\sqrt{50400}=\sqrt{3600*14}=\sqrt{3600}*\sqrt{14}=60\sqrt{14}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{14}}{2*-30}=\frac{0-60\sqrt{14}}{-60}
=-\frac{60\sqrt{14}}{-60}
=-\frac{\sqrt{14}}{-1}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{14}}{2*-30}=\frac{0+60\sqrt{14}}{-60}
=\frac{60\sqrt{14}}{-60}
=\frac{\sqrt{14}}{-1}
$