7x^2+56x+67=0

Solution for 7x^2+56x+67=0 equation:

7x^2+56x+67=0

a = 7; b = 56; c = +67;
Δ = b2-4ac
Δ = 562-4·7·67
Δ = 1260
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:

$\sqrt{\Delta}=\sqrt{1260}=\sqrt{36*35}=\sqrt{36}*\sqrt{35}=6\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-6\sqrt{35}}{2*7}=\frac{-56-6\sqrt{35}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+6\sqrt{35}}{2*7}=\frac{-56+6\sqrt{35}}{14}
$