-12d-1/10d+5=0

Solution for -12d-1/10d+5=0 equation:

-12d-1/10d+5=0


Domain of the equation: 10d!=0

d!=0/10

d!=0

d∈R


We multiply all the terms by the denominator


-12d*10d+5*10d-1=0

Wy multiply elements

-120d^2+50d-1=0

a = -120; b = 50; c = -1;
Δ = b2-4ac
Δ = 502-4·(-120)·(-1)
Δ = 2020
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:

$\sqrt{\Delta}=\sqrt{2020}=\sqrt{4*505}=\sqrt{4}*\sqrt{505}=2\sqrt{505}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{505}}{2*-120}=\frac{-50-2\sqrt{505}}{-240}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{505}}{2*-120}=\frac{-50+2\sqrt{505}}{-240}
$