0=-2x^2+14x-15

Solution for 0=-2x^2+14x-15 equation:

0=-2x^2+14x-15

We move all terms to the left:

0-(-2x^2+14x-15)=0

We add all the numbers together, and all the variables

-(-2x^2+14x-15)=0

We get rid of parentheses

2x^2-14x+15=0

a = 2; b = -14; c = +15;
Δ = b2-4ac
Δ = -142-4·2·15
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{-(-14)-2\sqrt{19}}{2*2}=\frac{14-2\sqrt{19}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{19}}{2*2}=\frac{14+2\sqrt{19}}{4}
$