50x(x-1)=143-5x

Solution for 50x(x-1)=143-5x equation:

50x(x-1)=143-5x

We move all terms to the left:

50x(x-1)-(143-5x)=0

We add all the numbers together, and all the variables

50x(x-1)-(-5x+143)=0

We multiply parentheses

50x^2-50x-(-5x+143)=0

We get rid of parentheses

50x^2-50x+5x-143=0

We add all the numbers together, and all the variables

50x^2-45x-143=0

a = 50; b = -45; c = -143;
Δ = b2-4ac
Δ = -452-4·50·(-143)
Δ = 30625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{30625}=175$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-175}{2*50}=\frac{-130}{100}
=-1+3/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+175}{2*50}=\frac{220}{100}
=2+1/5
$