X2+28x+53=0

Solution for X2+28x+53=0 equation:

X2+28X+53=0

We add all the numbers together, and all the variables

X^2+28X+53=0

a = 1; b = 28; c = +53;
Δ = b2-4ac
Δ = 282-4·1·53
Δ = 572
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:

$\sqrt{\Delta}=\sqrt{572}=\sqrt{4*143}=\sqrt{4}*\sqrt{143}=2\sqrt{143}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{143}}{2*1}=\frac{-28-2\sqrt{143}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{143}}{2*1}=\frac{-28+2\sqrt{143}}{2}
$