4x+11=50-2x2

Solution for 4x+11=50-2x2 equation:

4x+11=50-2x^2

We move all terms to the left:

4x+11-(50-2x^2)=0

We get rid of parentheses

2x^2+4x-50+11=0

We add all the numbers together, and all the variables

2x^2+4x-39=0

a = 2; b = 4; c = -39;
Δ = b2-4ac
Δ = 42-4·2·(-39)
Δ = 328
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:

$\sqrt{\Delta}=\sqrt{328}=\sqrt{4*82}=\sqrt{4}*\sqrt{82}=2\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{82}}{2*2}=\frac{-4-2\sqrt{82}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{82}}{2*2}=\frac{-4+2\sqrt{82}}{4}
$