5x^2+28x=-1

Solution for 5x^2+28x=-1 equation:

5x^2+28x=-1

We move all terms to the left:

5x^2+28x-(-1)=0

We add all the numbers together, and all the variables

5x^2+28x+1=0

a = 5; b = 28; c = +1;
Δ = b2-4ac
Δ = 282-4·5·1
Δ = 764
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:

$\sqrt{\Delta}=\sqrt{764}=\sqrt{4*191}=\sqrt{4}*\sqrt{191}=2\sqrt{191}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{191}}{2*5}=\frac{-28-2\sqrt{191}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{191}}{2*5}=\frac{-28+2\sqrt{191}}{10}
$