4x^2+30=2x+50

Solution for 4x^2+30=2x+50 equation:

4x^2+30=2x+50

We move all terms to the left:

4x^2+30-(2x+50)=0

We get rid of parentheses

4x^2-2x-50+30=0

We add all the numbers together, and all the variables

4x^2-2x-20=0

a = 4; b = -2; c = -20;
Δ = b2-4ac
Δ = -22-4·4·(-20)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-18}{2*4}=\frac{-16}{8}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+18}{2*4}=\frac{20}{8}
=2+1/2
$