/9e+4=-5e+14+13e

Solution for /9e+4=-5e+14+13e equation:

/9e+4=-5e+14+13e

We move all terms to the left:

/9e+4-(-5e+14+13e)=0


Domain of the equation: 9e!=0

e!=0/9

e!=0

e∈R


We add all the numbers together, and all the variables

/9e-(8e+14)+4=0

We get rid of parentheses

/9e-8e-14+4=0

We multiply all the terms by the denominator


-8e*9e-14*9e+4*9e+=0

We add all the numbers together, and all the variables

-8e*9e-14*9e+4*9e=0

Wy multiply elements

-72e^2-126e+36e=0

We add all the numbers together, and all the variables

-72e^2-90e=0

a = -72; b = -90; c = 0;
Δ = b2-4ac
Δ = -902-4·(-72)·0
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-90}{2*-72}=\frac{0}{-144}
=0
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+90}{2*-72}=\frac{180}{-144}
=-1+1/4
$