1/4x+7/16x=-131/2

Solution for 1/4x+7/16x=-131/2 equation:

1/4x+7/16x=-131/2

We move all terms to the left:

1/4x+7/16x-(-131/2)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 16x!=0

x!=0/16

x!=0

x∈R


We get rid of parentheses

1/4x+7/16x+131/2=0

We calculate fractions


8384x^2/256x^2+64x/256x^2+112x/256x^2=0

We multiply all the terms by the denominator


8384x^2+64x+112x=0

We add all the numbers together, and all the variables

8384x^2+176x=0

a = 8384; b = 176; c = 0;
Δ = b2-4ac
Δ = 1762-4·8384·0
Δ = 30976
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{30976}=176$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(176)-176}{2*8384}=\frac{-352}{16768}
=-11/524
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(176)+176}{2*8384}=\frac{0}{16768}
=0
$