14x+x^2=195

Solution for 14x+x^2=195 equation:

14x+x^2=195

We move all terms to the left:

14x+x^2-(195)=0

a = 1; b = 14; c = -195;
Δ = b2-4ac
Δ = 142-4·1·(-195)
Δ = 976
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:

$\sqrt{\Delta}=\sqrt{976}=\sqrt{16*61}=\sqrt{16}*\sqrt{61}=4\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-4\sqrt{61}}{2*1}=\frac{-14-4\sqrt{61}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+4\sqrt{61}}{2*1}=\frac{-14+4\sqrt{61}}{2}
$