1/4x+3=-5/8x-5

Solution for 1/4x+3=-5/8x-5 equation:

1/4x+3=-5/8x-5

We move all terms to the left:

1/4x+3-(-5/8x-5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x-5)!=0

x∈R


We get rid of parentheses

1/4x+5/8x+5+3=0

We calculate fractions


8x/32x^2+20x/32x^2+5+3=0

We add all the numbers together, and all the variables

8x/32x^2+20x/32x^2+8=0

We multiply all the terms by the denominator


8x+20x+8*32x^2=0

We add all the numbers together, and all the variables

28x+8*32x^2=0

Wy multiply elements

256x^2+28x=0

a = 256; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·256·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*256}=\frac{-56}{512}
=-7/64
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*256}=\frac{0}{512}
=0
$