(1/2)(5x+10)=12x-2

Solution for (1/2)(5x+10)=12x-2 equation:

(1/2)(5x+10)=12x-2

We move all terms to the left:

(1/2)(5x+10)-(12x-2)=0


Domain of the equation: 2)(5x+10)!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)(5x+10)-(12x-2)=0

We get rid of parentheses

(+1/2)(5x+10)-12x+2=0

We multiply parentheses ..

(+5x^2+1/2*10)-12x+2=0

We multiply all the terms by the denominator


(+5x^2+1-12x*2*10)+2*2*10)=0

We add all the numbers together, and all the variables

(+5x^2+1-12x*2*10)=0

We get rid of parentheses

5x^2-12x*2*10+1=0

Wy multiply elements

5x^2-240x*1+1=0

Wy multiply elements

5x^2-240x+1=0

a = 5; b = -240; c = +1;
Δ = b2-4ac
Δ = -2402-4·5·1
Δ = 57580
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:

$\sqrt{\Delta}=\sqrt{57580}=\sqrt{4*14395}=\sqrt{4}*\sqrt{14395}=2\sqrt{14395}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-2\sqrt{14395}}{2*5}=\frac{240-2\sqrt{14395}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+2\sqrt{14395}}{2*5}=\frac{240+2\sqrt{14395}}{10}
$