x^2-35x-147=0

Solution for x^2-35x-147=0 equation:

x^2-35x-147=0

a = 1; b = -35; c = -147;
Δ = b2-4ac
Δ = -352-4·1·(-147)
Δ = 1813
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:

$\sqrt{\Delta}=\sqrt{1813}=\sqrt{49*37}=\sqrt{49}*\sqrt{37}=7\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-7\sqrt{37}}{2*1}=\frac{35-7\sqrt{37}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+7\sqrt{37}}{2*1}=\frac{35+7\sqrt{37}}{2}
$