7/2x+1/2x=10+9/10x

Solution for 7/2x+1/2x=10+9/10x equation:

7/2x+1/2x=10+9/10x

We move all terms to the left:

7/2x+1/2x-(10+9/10x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

7/2x+1/2x-(9/10x+10)=0

We get rid of parentheses

7/2x+1/2x-9/10x-10=0

We calculate fractions


(10x+7)/20x^2+(-18x)/20x^2-10=0

We multiply all the terms by the denominator


(10x+7)+(-18x)-10*20x^2=0

Wy multiply elements

-200x^2+(10x+7)+(-18x)=0

We get rid of parentheses

-200x^2+10x-18x+7=0

We add all the numbers together, and all the variables

-200x^2-8x+7=0

a = -200; b = -8; c = +7;
Δ = b2-4ac
Δ = -82-4·(-200)·7
Δ = 5664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5664}=\sqrt{16*354}=\sqrt{16}*\sqrt{354}=4\sqrt{354}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{354}}{2*-200}=\frac{8-4\sqrt{354}}{-400}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{354}}{2*-200}=\frac{8+4\sqrt{354}}{-400}
$