2x(8-3x)-(2-7x)=12-(5-2x)

Solution for 2x(8-3x)-(2-7x)=12-(5-2x) equation:

2x(8-3x)-(2-7x)=12-(5-2x)

We move all terms to the left:

2x(8-3x)-(2-7x)-(12-(5-2x))=0

We add all the numbers together, and all the variables

2x(-3x+8)-(-7x+2)-(12-(-2x+5))=0

We multiply parentheses

-6x^2+16x-(-7x+2)-(12-(-2x+5))=0

We get rid of parentheses

-6x^2+16x+7x-(12-(-2x+5))-2=0


We calculate terms in parentheses: -(12-(-2x+5)), so:

12-(-2x+5)

determiningTheFunctionDomain
-(-2x+5)+12

We get rid of parentheses

2x-5+12

We add all the numbers together, and all the variables

2x+7

Back to the equation:

-(2x+7)


We add all the numbers together, and all the variables

-6x^2+23x-(2x+7)-2=0

We get rid of parentheses

-6x^2+23x-2x-7-2=0

We add all the numbers together, and all the variables

-6x^2+21x-9=0

a = -6; b = 21; c = -9;
Δ = b2-4ac
Δ = 212-4·(-6)·(-9)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-15}{2*-6}=\frac{-36}{-12}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+15}{2*-6}=\frac{-6}{-12}
=1/2
$