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

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

X=(2X-6)(X+7)

We move all terms to the left:

X-((2X-6)(X+7))=0

We multiply parentheses ..

-((+2X^2+14X-6X-42))+X=0


We calculate terms in parentheses: -((+2X^2+14X-6X-42)), so:

(+2X^2+14X-6X-42)

We get rid of parentheses

2X^2+14X-6X-42

We add all the numbers together, and all the variables

2X^2+8X-42

Back to the equation:

-(2X^2+8X-42)


We add all the numbers together, and all the variables

X-(2X^2+8X-42)=0

We get rid of parentheses

-2X^2+X-8X+42=0

We add all the numbers together, and all the variables

-2X^2-7X+42=0

a = -2; b = -7; c = +42;
Δ = b2-4ac
Δ = -72-4·(-2)·42
Δ = 385
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{385}}{2*-2}=\frac{7-\sqrt{385}}{-4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{385}}{2*-2}=\frac{7+\sqrt{385}}{-4}
$