X^2-14x-83=4

Solution for X^2-14x-83=4 equation:

X^2-14X-83=4

We move all terms to the left:

X^2-14X-83-(4)=0

We add all the numbers together, and all the variables

X^2-14X-87=0

a = 1; b = -14; c = -87;
Δ = b2-4ac
Δ = -142-4·1·(-87)
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-4\sqrt{34}}{2*1}=\frac{14-4\sqrt{34}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4\sqrt{34}}{2*1}=\frac{14+4\sqrt{34}}{2}
$