-13x^2+54x+147=0

Solution for -13x^2+54x+147=0 equation:

-13x^2+54x+147=0

a = -13; b = 54; c = +147;
Δ = b2-4ac
Δ = 542-4·(-13)·147
Δ = 10560
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:

$\sqrt{\Delta}=\sqrt{10560}=\sqrt{64*165}=\sqrt{64}*\sqrt{165}=8\sqrt{165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-8\sqrt{165}}{2*-13}=\frac{-54-8\sqrt{165}}{-26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+8\sqrt{165}}{2*-13}=\frac{-54+8\sqrt{165}}{-26}
$