(67+25x)x=300+25x

Solution for (67+25x)x=300+25x equation:

(67+25x)x=300+25x

We move all terms to the left:

(67+25x)x-(300+25x)=0

We add all the numbers together, and all the variables

(25x+67)x-(25x+300)=0

We multiply parentheses

25x^2+67x-(25x+300)=0

We get rid of parentheses

25x^2+67x-25x-300=0

We add all the numbers together, and all the variables

25x^2+42x-300=0

a = 25; b = 42; c = -300;
Δ = b2-4ac
Δ = 422-4·25·(-300)
Δ = 31764
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:

$\sqrt{\Delta}=\sqrt{31764}=\sqrt{4*7941}=\sqrt{4}*\sqrt{7941}=2\sqrt{7941}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{7941}}{2*25}=\frac{-42-2\sqrt{7941}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{7941}}{2*25}=\frac{-42+2\sqrt{7941}}{50}
$