144=x(x-50)

Solution for 144=x(x-50) equation:

144=x(x-50)

We move all terms to the left:

144-(x(x-50))=0


We calculate terms in parentheses: -(x(x-50)), so:

x(x-50)

We multiply parentheses

x^2-50x

Back to the equation:

-(x^2-50x)


We get rid of parentheses

-x^2+50x+144=0

We add all the numbers together, and all the variables

-1x^2+50x+144=0

a = -1; b = 50; c = +144;
Δ = b2-4ac
Δ = 502-4·(-1)·144
Δ = 3076
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:

$\sqrt{\Delta}=\sqrt{3076}=\sqrt{4*769}=\sqrt{4}*\sqrt{769}=2\sqrt{769}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{769}}{2*-1}=\frac{-50-2\sqrt{769}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{769}}{2*-1}=\frac{-50+2\sqrt{769}}{-2}
$