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 = 380
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:

$\sqrt{\Delta}=\sqrt{380}=\sqrt{4*95}=\sqrt{4}*\sqrt{95}=2\sqrt{95}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{95}}{2*2}=\frac{30-2\sqrt{95}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{95}}{2*2}=\frac{30+2\sqrt{95}}{4}
$