X2+14x-145=0

Solution for X2+14x-145=0 equation:

X2+14X-145=0

We add all the numbers together, and all the variables

X^2+14X-145=0

a = 1; b = 14; c = -145;
Δ = b2-4ac
Δ = 142-4·1·(-145)
Δ = 776
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:

$\sqrt{\Delta}=\sqrt{776}=\sqrt{4*194}=\sqrt{4}*\sqrt{194}=2\sqrt{194}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{194}}{2*1}=\frac{-14-2\sqrt{194}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{194}}{2*1}=\frac{-14+2\sqrt{194}}{2}
$