-7x+(1/2)(6x+8)-5x+12=-20

Solution for -7x+(1/2)(6x+8)-5x+12=-20 equation:

-7x+(1/2)(6x+8)-5x+12=-20

We move all terms to the left:

-7x+(1/2)(6x+8)-5x+12-(-20)=0


Domain of the equation: 2)(6x+8)!=0

x∈R


We add all the numbers together, and all the variables

-7x+(+1/2)(6x+8)-5x+12-(-20)=0

We add all the numbers together, and all the variables

-12x+(+1/2)(6x+8)+32=0

We multiply parentheses ..

(+6x^2+1/2*8)-12x+32=0

We multiply all the terms by the denominator


(+6x^2+1-12x*2*8)+32*2*8)=0

We add all the numbers together, and all the variables

(+6x^2+1-12x*2*8)=0

We get rid of parentheses

6x^2-12x*2*8+1=0

Wy multiply elements

6x^2-192x*8+1=0

Wy multiply elements

6x^2-1536x+1=0

a = 6; b = -1536; c = +1;
Δ = b2-4ac
Δ = -15362-4·6·1
Δ = 2359272
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:

$\sqrt{\Delta}=\sqrt{2359272}=\sqrt{4*589818}=\sqrt{4}*\sqrt{589818}=2\sqrt{589818}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1536)-2\sqrt{589818}}{2*6}=\frac{1536-2\sqrt{589818}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1536)+2\sqrt{589818}}{2*6}=\frac{1536+2\sqrt{589818}}{12}
$