1/2x+23=-1/4x-10

Solution for 1/2x+23=-1/4x-10 equation:

1/2x+23=-1/4x-10

We move all terms to the left:

1/2x+23-(-1/4x-10)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x-10)!=0

x∈R


We get rid of parentheses

1/2x+1/4x+10+23=0

We calculate fractions


4x/8x^2+2x/8x^2+10+23=0

We add all the numbers together, and all the variables

4x/8x^2+2x/8x^2+33=0

We multiply all the terms by the denominator


4x+2x+33*8x^2=0

We add all the numbers together, and all the variables

6x+33*8x^2=0

Wy multiply elements

264x^2+6x=0

a = 264; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·264·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*264}=\frac{-12}{528}
=-1/44
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*264}=\frac{0}{528}
=0
$