21x(31+x)=-52-3(13x+6x)-8(-x-15)

Solution for 21x(31+x)=-52-3(13x+6x)-8(-x-15) equation:

21x(31+x)=-52-3(13x+6x)-8(-x-15)

We move all terms to the left:

21x(31+x)-(-52-3(13x+6x)-8(-x-15))=0

We add all the numbers together, and all the variables

21x(x+31)-(-52-3(+19x)-8(-1x-15))=0

We multiply parentheses

21x^2+651x-(-52-3(+19x)-8(-1x-15))=0


We calculate terms in parentheses: -(-52-3(+19x)-8(-1x-15)), so:

-52-3(+19x)-8(-1x-15)

determiningTheFunctionDomain
-3(+19x)-8(-1x-15)-52

We multiply parentheses

-57x+8x+120-52

We add all the numbers together, and all the variables

-49x+68

Back to the equation:

-(-49x+68)


We get rid of parentheses

21x^2+651x+49x-68=0

We add all the numbers together, and all the variables

21x^2+700x-68=0

a = 21; b = 700; c = -68;
Δ = b2-4ac
Δ = 7002-4·21·(-68)
Δ = 495712
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:

$\sqrt{\Delta}=\sqrt{495712}=\sqrt{16*30982}=\sqrt{16}*\sqrt{30982}=4\sqrt{30982}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(700)-4\sqrt{30982}}{2*21}=\frac{-700-4\sqrt{30982}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(700)+4\sqrt{30982}}{2*21}=\frac{-700+4\sqrt{30982}}{42}
$