1/4x+2=-5/8x+-5

Solution for 1/4x+2=-5/8x+-5 equation:

1/4x+2=-5/8x+-5

We move all terms to the left:

1/4x+2-(-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 add all the numbers together, and all the variables

1/4x-(-5/8x-5)+2=0

We get rid of parentheses

1/4x+5/8x+5+2=0

We calculate fractions


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

We add all the numbers together, and all the variables

8x/32x^2+20x/32x^2+7=0

We multiply all the terms by the denominator


8x+20x+7*32x^2=0

We add all the numbers together, and all the variables

28x+7*32x^2=0

Wy multiply elements

224x^2+28x=0

a = 224; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·224·0
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*224}=\frac{-56}{448}
=-1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*224}=\frac{0}{448}
=0
$