2x^2+28x+17=-4

Solution for 2x^2+28x+17=-4 equation:

2x^2+28x+17=-4

We move all terms to the left:

2x^2+28x+17-(-4)=0

We add all the numbers together, and all the variables

2x^2+28x+21=0

a = 2; b = 28; c = +21;
Δ = b2-4ac
Δ = 282-4·2·21
Δ = 616
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:

$\sqrt{\Delta}=\sqrt{616}=\sqrt{4*154}=\sqrt{4}*\sqrt{154}=2\sqrt{154}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{154}}{2*2}=\frac{-28-2\sqrt{154}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{154}}{2*2}=\frac{-28+2\sqrt{154}}{4}
$