0=-7x2+4x+34

Solution for 0=-7x2+4x+34 equation:

0=-7x^2+4x+34

We move all terms to the left:

0-(-7x^2+4x+34)=0

We add all the numbers together, and all the variables

-(-7x^2+4x+34)=0

We get rid of parentheses

7x^2-4x-34=0

a = 7; b = -4; c = -34;
Δ = b2-4ac
Δ = -42-4·7·(-34)
Δ = 968
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:

$\sqrt{\Delta}=\sqrt{968}=\sqrt{484*2}=\sqrt{484}*\sqrt{2}=22\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-22\sqrt{2}}{2*7}=\frac{4-22\sqrt{2}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+22\sqrt{2}}{2*7}=\frac{4+22\sqrt{2}}{14}
$