0=2X^2+4x-15

Solution for 0=2X^2+4x-15 equation:

0=2X^2+4X-15

We move all terms to the left:

0-(2X^2+4X-15)=0

We add all the numbers together, and all the variables

-(2X^2+4X-15)=0

We get rid of parentheses

-2X^2-4X+15=0

a = -2; b = -4; c = +15;
Δ = b2-4ac
Δ = -42-4·(-2)·15
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{34}}{2*-2}=\frac{4-2\sqrt{34}}{-4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{34}}{2*-2}=\frac{4+2\sqrt{34}}{-4}
$