X^2-14x+5=-3

Solution for X^2-14x+5=-3 equation:

X^2-14X+5=-3

We move all terms to the left:

X^2-14X+5-(-3)=0

We add all the numbers together, and all the variables

X^2-14X+8=0

a = 1; b = -14; c = +8;
Δ = b2-4ac
Δ = -142-4·1·8
Δ = 164
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:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{41}}{2*1}=\frac{14-2\sqrt{41}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{41}}{2*1}=\frac{14+2\sqrt{41}}{2}
$