13x^2-108x+207=0

Solution for 13x^2-108x+207=0 equation:

13x^2-108x+207=0

a = 13; b = -108; c = +207;
Δ = b2-4ac
Δ = -1082-4·13·207
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-30}{2*13}=\frac{78}{26}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+30}{2*13}=\frac{138}{26}
=5+4/13
$