x=(1/2)(x-10+2x-3)

Solution for x=(1/2)(x-10+2x-3) equation:

x=(1/2)(x-10+2x-3)

We move all terms to the left:

x-((1/2)(x-10+2x-3))=0


Domain of the equation: 2)(x-10+2x-3))!=0

We move all terms containing x to the left, all other terms to the right

2)(x+2x-3))!=10

x∈R


We add all the numbers together, and all the variables

x-((+1/2)(3x-13))=0

We multiply parentheses ..

-((+3x^2+1/2*-13))+x=0

We multiply all the terms by the denominator


-((+3x^2+1+x*2*-13))=0


We calculate terms in parentheses: -((+3x^2+1+x*2*-13)), so:

(+3x^2+1+x*2*-13)

We get rid of parentheses

3x^2+x*2*+1-13

We add all the numbers together, and all the variables

3x^2+x*2*-12

Wy multiply elements

3x^2+2x^2-12

We add all the numbers together, and all the variables

5x^2-12

Back to the equation:

-(5x^2-12)


We get rid of parentheses

-5x^2+12=0

a = -5; b = 0; c = +12;
Δ = b2-4ac
Δ = 02-4·(-5)·12
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*-5}=\frac{0-4\sqrt{15}}{-10}
=-\frac{4\sqrt{15}}{-10}
=-\frac{2\sqrt{15}}{-5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*-5}=\frac{0+4\sqrt{15}}{-10}
=\frac{4\sqrt{15}}{-10}
=\frac{2\sqrt{15}}{-5}
$