x^2+45x=1000000

Solution for x^2+45x=1000000 equation:

x^2+45x=1000000

We move all terms to the left:

x^2+45x-(1000000)=0

a = 1; b = 45; c = -1000000;
Δ = b2-4ac
Δ = 452-4·1·(-1000000)
Δ = 4002025
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:

$\sqrt{\Delta}=\sqrt{4002025}=\sqrt{25*160081}=\sqrt{25}*\sqrt{160081}=5\sqrt{160081}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-5\sqrt{160081}}{2*1}=\frac{-45-5\sqrt{160081}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+5\sqrt{160081}}{2*1}=\frac{-45+5\sqrt{160081}}{2}
$