62x(X+20)+90X=2000

Solution for 62x(X+20)+90X=2000 equation:

62x(x+20)+90x=2000

We move all terms to the left:

62x(x+20)+90x-(2000)=0

We add all the numbers together, and all the variables

90x+62x(x+20)-2000=0

We multiply parentheses

62x^2+90x+1240x-2000=0

We add all the numbers together, and all the variables

62x^2+1330x-2000=0

a = 62; b = 1330; c = -2000;
Δ = b2-4ac
Δ = 13302-4·62·(-2000)
Δ = 2264900
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:

$\sqrt{\Delta}=\sqrt{2264900}=\sqrt{100*22649}=\sqrt{100}*\sqrt{22649}=10\sqrt{22649}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1330)-10\sqrt{22649}}{2*62}=\frac{-1330-10\sqrt{22649}}{124}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1330)+10\sqrt{22649}}{2*62}=\frac{-1330+10\sqrt{22649}}{124}
$