13x^2-42x-18=0

Solution for 13x^2-42x-18=0 equation:

13x^2-42x-18=0

a = 13; b = -42; c = -18;
Δ = b2-4ac
Δ = -422-4·13·(-18)
Δ = 2700
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:

$\sqrt{\Delta}=\sqrt{2700}=\sqrt{900*3}=\sqrt{900}*\sqrt{3}=30\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-30\sqrt{3}}{2*13}=\frac{42-30\sqrt{3}}{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+30\sqrt{3}}{2*13}=\frac{42+30\sqrt{3}}{26}
$