4x+50=2x^2+x

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

4x+50=2x^2+x

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -2; b = 3; c = +50;
Δ = b2-4ac
Δ = 32-4·(-2)·50
Δ = 409
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{409}}{2*-2}=\frac{-3-\sqrt{409}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{409}}{2*-2}=\frac{-3+\sqrt{409}}{-4}
$