(84)+(x^2+6)=90,x

Solution for (84)+(x^2+6)=90,x equation:

(84)+(x^2+6)=90.x

We move all terms to the left:

(84)+(x^2+6)-(90.x)=0

We add all the numbers together, and all the variables

(x^2+6)-(+90.x)+84=0

We get rid of parentheses

x^2-90.x+6+84=0

We add all the numbers together, and all the variables

x^2-90x+90=0

a = 1; b = -90; c = +90;
Δ = b2-4ac
Δ = -902-4·1·90
Δ = 7740
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:

$\sqrt{\Delta}=\sqrt{7740}=\sqrt{36*215}=\sqrt{36}*\sqrt{215}=6\sqrt{215}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-6\sqrt{215}}{2*1}=\frac{90-6\sqrt{215}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+6\sqrt{215}}{2*1}=\frac{90+6\sqrt{215}}{2}
$