x*x+(x+60)(x+60)=90000

Solution for x*x+(x+60)(x+60)=90000 equation:

x*x+(x+60)(x+60)=90000

We move all terms to the left:

x*x+(x+60)(x+60)-(90000)=0

Wy multiply elements

x^2+(x+60)(x+60)-90000=0

We multiply parentheses ..

x^2+(+x^2+60x+60x+3600)-90000=0

We get rid of parentheses

x^2+x^2+60x+60x+3600-90000=0

We add all the numbers together, and all the variables

2x^2+120x-86400=0

a = 2; b = 120; c = -86400;
Δ = b2-4ac
Δ = 1202-4·2·(-86400)
Δ = 705600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{705600}=840$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-840}{2*2}=\frac{-960}{4}
=-240
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+840}{2*2}=\frac{720}{4}
=180
$