6x(x+7)=77

Solution for 6x(x+7)=77 equation:

6x(x+7)=77

We move all terms to the left:

6x(x+7)-(77)=0

We multiply parentheses

6x^2+42x-77=0

a = 6; b = 42; c = -77;
Δ = b2-4ac
Δ = 422-4·6·(-77)
Δ = 3612
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:

$\sqrt{\Delta}=\sqrt{3612}=\sqrt{4*903}=\sqrt{4}*\sqrt{903}=2\sqrt{903}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{903}}{2*6}=\frac{-42-2\sqrt{903}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{903}}{2*6}=\frac{-42+2\sqrt{903}}{12}
$