45/78k+-45=487536k

Solution for 45/78k+-45=487536k equation:

45/78k+-45=487536k

We move all terms to the left:

45/78k+-45-(487536k)=0


Domain of the equation: 78k!=0

k!=0/78

k!=0

k∈R


We add all the numbers together, and all the variables

-487536k+45/78k=0

We multiply all the terms by the denominator


-487536k*78k+45=0

Wy multiply elements

-38027808k^2+45=0

a = -38027808; b = 0; c = +45;
Δ = b2-4ac
Δ = 02-4·(-38027808)·45
Δ = 6845005440
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6845005440}=\sqrt{5184*1320410}=\sqrt{5184}*\sqrt{1320410}=72\sqrt{1320410}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72\sqrt{1320410}}{2*-38027808}=\frac{0-72\sqrt{1320410}}{-76055616}
=-\frac{72\sqrt{1320410}}{-76055616}
=-\frac{\sqrt{1320410}}{-1056328}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72\sqrt{1320410}}{2*-38027808}=\frac{0+72\sqrt{1320410}}{-76055616}
=\frac{72\sqrt{1320410}}{-76055616}
=\frac{\sqrt{1320410}}{-1056328}
$