13x^2+145x-64=0

Solution for 13x^2+145x-64=0 equation:

13x^2+145x-64=0

a = 13; b = 145; c = -64;
Δ = b2-4ac
Δ = 1452-4·13·(-64)
Δ = 24353
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:

$\sqrt{\Delta}=\sqrt{24353}=\sqrt{49*497}=\sqrt{49}*\sqrt{497}=7\sqrt{497}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(145)-7\sqrt{497}}{2*13}=\frac{-145-7\sqrt{497}}{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(145)+7\sqrt{497}}{2*13}=\frac{-145+7\sqrt{497}}{26}
$