45,000+15x+0.3x^2=605x-0.7x^2

Solution for 45,000+15x+0.3x^2=605x-0.7x^2 equation:

45.000+15x+0.3x^2=605x-0.7x^2

We move all terms to the left:

45.000+15x+0.3x^2-(605x-0.7x^2)=0

We add all the numbers together, and all the variables

0.3x^2-(605x-0.7x^2)+15x+45=0

We get rid of parentheses

0.3x^2+0.7x^2-605x+15x+45=0

We add all the numbers together, and all the variables

x^2-590x+45=0

a = 1; b = -590; c = +45;
Δ = b2-4ac
Δ = -5902-4·1·45
Δ = 347920
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:

$\sqrt{\Delta}=\sqrt{347920}=\sqrt{16*21745}=\sqrt{16}*\sqrt{21745}=4\sqrt{21745}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-590)-4\sqrt{21745}}{2*1}=\frac{590-4\sqrt{21745}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-590)+4\sqrt{21745}}{2*1}=\frac{590+4\sqrt{21745}}{2}
$