7x^2+39x+9=0

Solution for 7x^2+39x+9=0 equation:

7x^2+39x+9=0

a = 7; b = 39; c = +9;
Δ = b2-4ac
Δ = 392-4·7·9
Δ = 1269
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:

$\sqrt{\Delta}=\sqrt{1269}=\sqrt{9*141}=\sqrt{9}*\sqrt{141}=3\sqrt{141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-3\sqrt{141}}{2*7}=\frac{-39-3\sqrt{141}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+3\sqrt{141}}{2*7}=\frac{-39+3\sqrt{141}}{14}
$