3x^2-4x=50+x

Solution for 3x^2-4x=50+x equation:

3x^2-4x=50+x

We move all terms to the left:

3x^2-4x-(50+x)=0

We add all the numbers together, and all the variables

3x^2-4x-(x+50)=0

We get rid of parentheses

3x^2-4x-x-50=0

We add all the numbers together, and all the variables

3x^2-5x-50=0

a = 3; b = -5; c = -50;
Δ = b2-4ac
Δ = -52-4·3·(-50)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-25}{2*3}=\frac{-20}{6}
=-3+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+25}{2*3}=\frac{30}{6}
=5
$