(x2+5x)2-20(x2+5x)=-84

Solution for (x2+5x)2-20(x2+5x)=-84 equation:

(x2+5x)2-20(x2+5x)=-84

We move all terms to the left:

(x2+5x)2-20(x2+5x)-(-84)=0

We add all the numbers together, and all the variables

(+x^2+5x)2-20(+x^2+5x)-(-84)=0

We add all the numbers together, and all the variables

(+x^2+5x)2-20(+x^2+5x)+84=0

We multiply parentheses

2x^2-20x^2+10x-100x+84=0

We add all the numbers together, and all the variables

-18x^2-90x+84=0

a = -18; b = -90; c = +84;
Δ = b2-4ac
Δ = -902-4·(-18)·84
Δ = 14148
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:

$\sqrt{\Delta}=\sqrt{14148}=\sqrt{36*393}=\sqrt{36}*\sqrt{393}=6\sqrt{393}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-6\sqrt{393}}{2*-18}=\frac{90-6\sqrt{393}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+6\sqrt{393}}{2*-18}=\frac{90+6\sqrt{393}}{-36}
$