(25+x)(10x)=1000

Solution for (25+x)(10x)=1000 equation:

(25+x)(10x)=1000

We move all terms to the left:

(25+x)(10x)-(1000)=0

We add all the numbers together, and all the variables

(x+25)10x-1000=0

We multiply parentheses

10x^2+250x-1000=0

a = 10; b = 250; c = -1000;
Δ = b2-4ac
Δ = 2502-4·10·(-1000)
Δ = 102500
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:

$\sqrt{\Delta}=\sqrt{102500}=\sqrt{2500*41}=\sqrt{2500}*\sqrt{41}=50\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(250)-50\sqrt{41}}{2*10}=\frac{-250-50\sqrt{41}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(250)+50\sqrt{41}}{2*10}=\frac{-250+50\sqrt{41}}{20}
$