0=-3x^2+14x+7

Solution for 0=-3x^2+14x+7 equation:

0=-3x^2+14x+7

We move all terms to the left:

0-(-3x^2+14x+7)=0

We add all the numbers together, and all the variables

-(-3x^2+14x+7)=0

We get rid of parentheses

3x^2-14x-7=0

a = 3; b = -14; c = -7;
Δ = b2-4ac
Δ = -142-4·3·(-7)
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{70}}{2*3}=\frac{14-2\sqrt{70}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{70}}{2*3}=\frac{14+2\sqrt{70}}{6}
$