d/20d+13-12d=-43

Solution for d/20d+13-12d=-43 equation:

d/20d+13-12d=-43

We move all terms to the left:

d/20d+13-12d-(-43)=0


Domain of the equation: 20d!=0

d!=0/20

d!=0

d∈R


We add all the numbers together, and all the variables

-12d+d/20d+56=0

We multiply all the terms by the denominator


-12d*20d+d+56*20d=0

We add all the numbers together, and all the variables

d-12d*20d+56*20d=0

Wy multiply elements

-240d^2+d+1120d=0

We add all the numbers together, and all the variables

-240d^2+1121d=0

a = -240; b = 1121; c = 0;
Δ = b2-4ac
Δ = 11212-4·(-240)·0
Δ = 1256641
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1256641}=1121$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1121)-1121}{2*-240}=\frac{-2242}{-480}
=4+161/240
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1121)+1121}{2*-240}=\frac{0}{-480}
=0
$