X=(3x-23)(2x+37)

Solution for X=(3x-23)(2x+37) equation:

X=(3X-23)(2X+37)

We move all terms to the left:

X-((3X-23)(2X+37))=0

We multiply parentheses ..

-((+6X^2+111X-46X-851))+X=0


We calculate terms in parentheses: -((+6X^2+111X-46X-851)), so:

(+6X^2+111X-46X-851)

We get rid of parentheses

6X^2+111X-46X-851

We add all the numbers together, and all the variables

6X^2+65X-851

Back to the equation:

-(6X^2+65X-851)


We add all the numbers together, and all the variables

X-(6X^2+65X-851)=0

We get rid of parentheses

-6X^2+X-65X+851=0

We add all the numbers together, and all the variables

-6X^2-64X+851=0

a = -6; b = -64; c = +851;
Δ = b2-4ac
Δ = -642-4·(-6)·851
Δ = 24520
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:

$\sqrt{\Delta}=\sqrt{24520}=\sqrt{4*6130}=\sqrt{4}*\sqrt{6130}=2\sqrt{6130}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-2\sqrt{6130}}{2*-6}=\frac{64-2\sqrt{6130}}{-12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+2\sqrt{6130}}{2*-6}=\frac{64+2\sqrt{6130}}{-12}
$