47=-5x-3x(-2x-13)

Solution for 47=-5x-3x(-2x-13) equation:

47=-5x-3x(-2x-13)

We move all terms to the left:

47-(-5x-3x(-2x-13))=0


We calculate terms in parentheses: -(-5x-3x(-2x-13)), so:

-5x-3x(-2x-13)

We multiply parentheses

6x^2-5x+39x

We add all the numbers together, and all the variables

6x^2+34x

Back to the equation:

-(6x^2+34x)


We get rid of parentheses

-6x^2-34x+47=0

a = -6; b = -34; c = +47;
Δ = b2-4ac
Δ = -342-4·(-6)·47
Δ = 2284
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:

$\sqrt{\Delta}=\sqrt{2284}=\sqrt{4*571}=\sqrt{4}*\sqrt{571}=2\sqrt{571}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{571}}{2*-6}=\frac{34-2\sqrt{571}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{571}}{2*-6}=\frac{34+2\sqrt{571}}{-12}
$