50+x(3*50+x)=1000

Solution for 50+x(3*50+x)=1000 equation:

50+x(3*50+x)=1000

We move all terms to the left:

50+x(3*50+x)-(1000)=0

We add all the numbers together, and all the variables

x(x+150)+50-1000=0

We add all the numbers together, and all the variables

x(x+150)-950=0

We multiply parentheses

x^2+150x-950=0

a = 1; b = 150; c = -950;
Δ = b2-4ac
Δ = 1502-4·1·(-950)
Δ = 26300
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:

$\sqrt{\Delta}=\sqrt{26300}=\sqrt{100*263}=\sqrt{100}*\sqrt{263}=10\sqrt{263}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-10\sqrt{263}}{2*1}=\frac{-150-10\sqrt{263}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+10\sqrt{263}}{2*1}=\frac{-150+10\sqrt{263}}{2}
$