X^2+4x-133=0

Solution for X^2+4x-133=0 equation:

X^2+4X-133=0

a = 1; b = 4; c = -133;
Δ = b2-4ac
Δ = 42-4·1·(-133)
Δ = 548
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:

$\sqrt{\Delta}=\sqrt{548}=\sqrt{4*137}=\sqrt{4}*\sqrt{137}=2\sqrt{137}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{137}}{2*1}=\frac{-4-2\sqrt{137}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{137}}{2*1}=\frac{-4+2\sqrt{137}}{2}
$