-4(3/4e+2)=7+1/2e-8

Solution for -4(3/4e+2)=7+1/2e-8 equation:

-4(3/4e+2)=7+1/2e-8

We move all terms to the left:

-4(3/4e+2)-(7+1/2e-8)=0


Domain of the equation: 4e+2)!=0

e∈R



Domain of the equation: 2e-8)!=0

e∈R


We add all the numbers together, and all the variables

-4(3/4e+2)-(1/2e-1)=0

We multiply parentheses

-12e-(1/2e-1)-8=0

We get rid of parentheses

-12e-1/2e+1-8=0

We multiply all the terms by the denominator


-12e*2e+1*2e-8*2e-1=0

Wy multiply elements

-24e^2+2e-16e-1=0

We add all the numbers together, and all the variables

-24e^2-14e-1=0

a = -24; b = -14; c = -1;
Δ = b2-4ac
Δ = -142-4·(-24)·(-1)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-10}{2*-24}=\frac{4}{-48}
=-1/12
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+10}{2*-24}=\frac{24}{-48}
=-1/2
$