X=(6x-4)(4x+14)

Solution for X=(6x-4)(4x+14) equation:

X=(6X-4)(4X+14)

We move all terms to the left:

X-((6X-4)(4X+14))=0

We multiply parentheses ..

-((+24X^2+84X-16X-56))+X=0


We calculate terms in parentheses: -((+24X^2+84X-16X-56)), so:

(+24X^2+84X-16X-56)

We get rid of parentheses

24X^2+84X-16X-56

We add all the numbers together, and all the variables

24X^2+68X-56

Back to the equation:

-(24X^2+68X-56)


We add all the numbers together, and all the variables

X-(24X^2+68X-56)=0

We get rid of parentheses

-24X^2+X-68X+56=0

We add all the numbers together, and all the variables

-24X^2-67X+56=0

a = -24; b = -67; c = +56;
Δ = b2-4ac
Δ = -672-4·(-24)·56
Δ = 9865
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{-(-67)-\sqrt{9865}}{2*-24}=\frac{67-\sqrt{9865}}{-48}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-67)+\sqrt{9865}}{2*-24}=\frac{67+\sqrt{9865}}{-48}
$