(1/2)(10x+20)=15x-10

Solution for (1/2)(10x+20)=15x-10 equation:

(1/2)(10x+20)=15x-10

We move all terms to the left:

(1/2)(10x+20)-(15x-10)=0


Domain of the equation: 2)(10x+20)!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)(10x+20)-(15x-10)=0

We get rid of parentheses

(+1/2)(10x+20)-15x+10=0

We multiply parentheses ..

(+10x^2+1/2*20)-15x+10=0

We multiply all the terms by the denominator


(+10x^2+1-15x*2*20)+10*2*20)=0

We add all the numbers together, and all the variables

(+10x^2+1-15x*2*20)=0

We get rid of parentheses

10x^2-15x*2*20+1=0

Wy multiply elements

10x^2-600x*2+1=0

Wy multiply elements

10x^2-1200x+1=0

a = 10; b = -1200; c = +1;
Δ = b2-4ac
Δ = -12002-4·10·1
Δ = 1439960
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:

$\sqrt{\Delta}=\sqrt{1439960}=\sqrt{4*359990}=\sqrt{4}*\sqrt{359990}=2\sqrt{359990}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1200)-2\sqrt{359990}}{2*10}=\frac{1200-2\sqrt{359990}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1200)+2\sqrt{359990}}{2*10}=\frac{1200+2\sqrt{359990}}{20}
$