X=(2x-7)(3x-1)=(2x-5)(3x+5)

Solution for X=(2x-7)(3x-1)=(2x-5)(3x+5) equation:

X=(2X-7)(3X-1)=(2X-5)(3X+5)

We move all terms to the left:

X-((2X-7)(3X-1))=0

We multiply parentheses ..

-((+6X^2-2X-21X+7))+X=0


We calculate terms in parentheses: -((+6X^2-2X-21X+7)), so:

(+6X^2-2X-21X+7)

We get rid of parentheses

6X^2-2X-21X+7

We add all the numbers together, and all the variables

6X^2-23X+7

Back to the equation:

-(6X^2-23X+7)


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-6X^2+24X-7=0

a = -6; b = 24; c = -7;
Δ = b2-4ac
Δ = 242-4·(-6)·(-7)
Δ = 408
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:

$\sqrt{\Delta}=\sqrt{408}=\sqrt{4*102}=\sqrt{4}*\sqrt{102}=2\sqrt{102}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{102}}{2*-6}=\frac{-24-2\sqrt{102}}{-12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{102}}{2*-6}=\frac{-24+2\sqrt{102}}{-12}
$