1/2x+10=-1/4x+53

Solution for 1/2x+10=-1/4x+53 equation:

1/2x+10=-1/4x+53

We move all terms to the left:

1/2x+10-(-1/4x+53)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x+53)!=0

x∈R


We get rid of parentheses

1/2x+1/4x-53+10=0

We calculate fractions


4x/8x^2+2x/8x^2-53+10=0

We add all the numbers together, and all the variables

4x/8x^2+2x/8x^2-43=0

We multiply all the terms by the denominator


4x+2x-43*8x^2=0

We add all the numbers together, and all the variables

6x-43*8x^2=0

Wy multiply elements

-344x^2+6x=0

a = -344; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-344)·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*-344}=\frac{-12}{-688}
=3/172
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-344}=\frac{0}{-688}
=0
$