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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


8x/16x^2+10x/16x^2+5+2=0

We add all the numbers together, and all the variables

8x/16x^2+10x/16x^2+7=0

We multiply all the terms by the denominator


8x+10x+7*16x^2=0

We add all the numbers together, and all the variables

18x+7*16x^2=0

Wy multiply elements

112x^2+18x=0

a = 112; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·112·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*112}=\frac{-36}{224}
=-9/56
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*112}=\frac{0}{224}
=0
$