X^2+14x=45=0

Solution for X^2+14x=45=0 equation:

X^2+14X=45=0

We move all terms to the left:

X^2+14X-(45)=0

a = 1; b = 14; c = -45;
Δ = b2-4ac
Δ = 142-4·1·(-45)
Δ = 376
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:

$\sqrt{\Delta}=\sqrt{376}=\sqrt{4*94}=\sqrt{4}*\sqrt{94}=2\sqrt{94}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{94}}{2*1}=\frac{-14-2\sqrt{94}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{94}}{2*1}=\frac{-14+2\sqrt{94}}{2}
$