7x^2+54x+67=0

Solution for 7x^2+54x+67=0 equation:

7x^2+54x+67=0

a = 7; b = 54; c = +67;
Δ = b2-4ac
Δ = 542-4·7·67
Δ = 1040
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:

$\sqrt{\Delta}=\sqrt{1040}=\sqrt{16*65}=\sqrt{16}*\sqrt{65}=4\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-4\sqrt{65}}{2*7}=\frac{-54-4\sqrt{65}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+4\sqrt{65}}{2*7}=\frac{-54+4\sqrt{65}}{14}
$