X=3(5x+13)(4x-3)

Solution for X=3(5x+13)(4x-3) equation:

X=3(5X+13)(4X-3)

We move all terms to the left:

X-(3(5X+13)(4X-3))=0

We multiply parentheses ..

-(3(+20X^2-15X+52X-39))+X=0


We calculate terms in parentheses: -(3(+20X^2-15X+52X-39)), so:

3(+20X^2-15X+52X-39)

We multiply parentheses

60X^2-45X+156X-117

We add all the numbers together, and all the variables

60X^2+111X-117

Back to the equation:

-(60X^2+111X-117)


We add all the numbers together, and all the variables

X-(60X^2+111X-117)=0

We get rid of parentheses

-60X^2+X-111X+117=0

We add all the numbers together, and all the variables

-60X^2-110X+117=0

a = -60; b = -110; c = +117;
Δ = b2-4ac
Δ = -1102-4·(-60)·117
Δ = 40180
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:

$\sqrt{\Delta}=\sqrt{40180}=\sqrt{196*205}=\sqrt{196}*\sqrt{205}=14\sqrt{205}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-14\sqrt{205}}{2*-60}=\frac{110-14\sqrt{205}}{-120}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+14\sqrt{205}}{2*-60}=\frac{110+14\sqrt{205}}{-120}
$