(2x-8)=(2x+7)(x-6)

Solution for (2x-8)=(2x+7)(x-6) equation:

(2x-8)=(2x+7)(x-6)

We move all terms to the left:

(2x-8)-((2x+7)(x-6))=0

We get rid of parentheses

2x-((2x+7)(x-6))-8=0

We multiply parentheses ..

-((+2x^2-12x+7x-42))+2x-8=0


We calculate terms in parentheses: -((+2x^2-12x+7x-42)), so:

(+2x^2-12x+7x-42)

We get rid of parentheses

2x^2-12x+7x-42

We add all the numbers together, and all the variables

2x^2-5x-42

Back to the equation:

-(2x^2-5x-42)


We add all the numbers together, and all the variables

2x-(2x^2-5x-42)-8=0

We get rid of parentheses

-2x^2+2x+5x+42-8=0

We add all the numbers together, and all the variables

-2x^2+7x+34=0

a = -2; b = 7; c = +34;
Δ = b2-4ac
Δ = 72-4·(-2)·34
Δ = 321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{321}}{2*-2}=\frac{-7-\sqrt{321}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{321}}{2*-2}=\frac{-7+\sqrt{321}}{-4}
$