2x^2+45x+100=1000

Solution for 2x^2+45x+100=1000 equation:

2x^2+45x+100=1000

We move all terms to the left:

2x^2+45x+100-(1000)=0

We add all the numbers together, and all the variables

2x^2+45x-900=0

a = 2; b = 45; c = -900;
Δ = b2-4ac
Δ = 452-4·2·(-900)
Δ = 9225
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:

$\sqrt{\Delta}=\sqrt{9225}=\sqrt{225*41}=\sqrt{225}*\sqrt{41}=15\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-15\sqrt{41}}{2*2}=\frac{-45-15\sqrt{41}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+15\sqrt{41}}{2*2}=\frac{-45+15\sqrt{41}}{4}
$