X=(3x+50)(6x-10)

Solution for X=(3x+50)(6x-10) equation:

X=(3X+50)(6X-10)

We move all terms to the left:

X-((3X+50)(6X-10))=0

We multiply parentheses ..

-((+18X^2-30X+300X-500))+X=0


We calculate terms in parentheses: -((+18X^2-30X+300X-500)), so:

(+18X^2-30X+300X-500)

We get rid of parentheses

18X^2-30X+300X-500

We add all the numbers together, and all the variables

18X^2+270X-500

Back to the equation:

-(18X^2+270X-500)


We add all the numbers together, and all the variables

X-(18X^2+270X-500)=0

We get rid of parentheses

-18X^2+X-270X+500=0

We add all the numbers together, and all the variables

-18X^2-269X+500=0

a = -18; b = -269; c = +500;
Δ = b2-4ac
Δ = -2692-4·(-18)·500
Δ = 108361
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{-(-269)-\sqrt{108361}}{2*-18}=\frac{269-\sqrt{108361}}{-36}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-269)+\sqrt{108361}}{2*-18}=\frac{269+\sqrt{108361}}{-36}
$