(5x+50)+(25x^2)=250^2

Solution for (5x+50)+(25x^2)=250^2 equation:

(5x+50)+(25x^2)=250^2

We move all terms to the left:

(5x+50)+(25x^2)-(250^2)=0

determiningTheFunctionDomain
25x^2+(5x+50)-250^2=0

We add all the numbers together, and all the variables

25x^2+(5x+50)-62500=0

We get rid of parentheses

25x^2+5x+50-62500=0

We add all the numbers together, and all the variables

25x^2+5x-62450=0

a = 25; b = 5; c = -62450;
Δ = b2-4ac
Δ = 52-4·25·(-62450)
Δ = 6245025
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:

$\sqrt{\Delta}=\sqrt{6245025}=\sqrt{25*249801}=\sqrt{25}*\sqrt{249801}=5\sqrt{249801}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{249801}}{2*25}=\frac{-5-5\sqrt{249801}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{249801}}{2*25}=\frac{-5+5\sqrt{249801}}{50}
$