7x^2-14x-39=-9

Solution for 7x^2-14x-39=-9 equation:

7x^2-14x-39=-9

We move all terms to the left:

7x^2-14x-39-(-9)=0

We add all the numbers together, and all the variables

7x^2-14x-30=0

a = 7; b = -14; c = -30;
Δ = b2-4ac
Δ = -142-4·7·(-30)
Δ = 1036
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:

$\sqrt{\Delta}=\sqrt{1036}=\sqrt{4*259}=\sqrt{4}*\sqrt{259}=2\sqrt{259}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{259}}{2*7}=\frac{14-2\sqrt{259}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{259}}{2*7}=\frac{14+2\sqrt{259}}{14}
$