47-x(3x+4)=2(17-2x)-62.

Solution for 47-x(3x+4)=2(17-2x)-62. equation:

47-x(3x+4)=2(17-2x)-62.

We move all terms to the left:

47-x(3x+4)-(2(17-2x)-62.)=0

We add all the numbers together, and all the variables

-x(3x+4)-(2(-2x+17)-62.)+47=0

We multiply parentheses

-3x^2-4x-(2(-2x+17)-62.)+47=0


We calculate terms in parentheses: -(2(-2x+17)-62.), so:

2(-2x+17)-62.

We add all the numbers together, and all the variables

2(-2x+17)-62

We multiply parentheses

-4x+34-62

We add all the numbers together, and all the variables

-4x-28

Back to the equation:

-(-4x-28)


We get rid of parentheses

-3x^2-4x+4x+28+47=0

We add all the numbers together, and all the variables

-3x^2+75=0

a = -3; b = 0; c = +75;
Δ = b2-4ac
Δ = 02-4·(-3)·75
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30}{2*-3}=\frac{-30}{-6}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30}{2*-3}=\frac{30}{-6}
=-5
$