X^2-10x-146=0

Solution for X^2-10x-146=0 equation:

X^2-10X-146=0

a = 1; b = -10; c = -146;
Δ = b2-4ac
Δ = -102-4·1·(-146)
Δ = 684
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:

$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6\sqrt{19}}{2*1}=\frac{10-6\sqrt{19}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6\sqrt{19}}{2*1}=\frac{10+6\sqrt{19}}{2}
$