2x+10,5x-20=10+1/2x

Solution for 2x+10,5x-20=10+1/2x equation:

2x+10.5x-20=10+1/2x

We move all terms to the left:

2x+10.5x-20-(10+1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x+10.5x-(1/2x+10)-20=0

We add all the numbers together, and all the variables

12.5x-(1/2x+10)-20=0

We get rid of parentheses

12.5x-1/2x-10-20=0

We multiply all the terms by the denominator


(12.5x)*2x-10*2x-20*2x-1=0

We add all the numbers together, and all the variables

(+12.5x)*2x-10*2x-20*2x-1=0

We multiply parentheses

24x^2-10*2x-20*2x-1=0

Wy multiply elements

24x^2-20x-40x-1=0

We add all the numbers together, and all the variables

24x^2-60x-1=0

a = 24; b = -60; c = -1;
Δ = b2-4ac
Δ = -602-4·24·(-1)
Δ = 3696
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:

$\sqrt{\Delta}=\sqrt{3696}=\sqrt{16*231}=\sqrt{16}*\sqrt{231}=4\sqrt{231}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{231}}{2*24}=\frac{60-4\sqrt{231}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{231}}{2*24}=\frac{60+4\sqrt{231}}{48}
$