x(7x-200)=300

Solution for x(7x-200)=300 equation:

x(7x-200)=300

We move all terms to the left:

x(7x-200)-(300)=0

We multiply parentheses

7x^2-200x-300=0

a = 7; b = -200; c = -300;
Δ = b2-4ac
Δ = -2002-4·7·(-300)
Δ = 48400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{48400}=220$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-220}{2*7}=\frac{-20}{14}
=-1+3/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+220}{2*7}=\frac{420}{14}
=30
$