2(x^2-3x-2.5)=0

Solution for 2(x^2-3x-2.5)=0 equation:

2(x^2-3x-2.5)=0

We multiply parentheses

2x^2-6x-5=0

a = 2; b = -6; c = -5;
Δ = b2-4ac
Δ = -62-4·2·(-5)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{19}}{2*2}=\frac{6-2\sqrt{19}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{19}}{2*2}=\frac{6+2\sqrt{19}}{4}
$