7x^2-34x=-7

Solution for 7x^2-34x=-7 equation:

7x^2-34x=-7

We move all terms to the left:

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

We add all the numbers together, and all the variables

7x^2-34x+7=0

a = 7; b = -34; c = +7;
Δ = b2-4ac
Δ = -342-4·7·7
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-8\sqrt{15}}{2*7}=\frac{34-8\sqrt{15}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+8\sqrt{15}}{2*7}=\frac{34+8\sqrt{15}}{14}
$