567(7-x)x=49

Solution for 567(7-x)x=49 equation:

567(7-x)x=49

We move all terms to the left:

567(7-x)x-(49)=0

We add all the numbers together, and all the variables

567(-1x+7)x-49=0

We multiply parentheses

-567x^2+3969x-49=0

a = -567; b = 3969; c = -49;
Δ = b2-4ac
Δ = 39692-4·(-567)·(-49)
Δ = 15641829
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:

$\sqrt{\Delta}=\sqrt{15641829}=\sqrt{3969*3941}=\sqrt{3969}*\sqrt{3941}=63\sqrt{3941}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3969)-63\sqrt{3941}}{2*-567}=\frac{-3969-63\sqrt{3941}}{-1134}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3969)+63\sqrt{3941}}{2*-567}=\frac{-3969+63\sqrt{3941}}{-1134}
$