2x^2+30x-65=0

Solution for 2x^2+30x-65=0 equation:

2x^2+30x-65=0

a = 2; b = 30; c = -65;
Δ = b2-4ac
Δ = 302-4·2·(-65)
Δ = 1420
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:

$\sqrt{\Delta}=\sqrt{1420}=\sqrt{4*355}=\sqrt{4}*\sqrt{355}=2\sqrt{355}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{355}}{2*2}=\frac{-30-2\sqrt{355}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{355}}{2*2}=\frac{-30+2\sqrt{355}}{4}
$