7x(4x-9)=77

Solution for 7x(4x-9)=77 equation:

7x(4x-9)=77

We move all terms to the left:

7x(4x-9)-(77)=0

We multiply parentheses

28x^2-63x-77=0

a = 28; b = -63; c = -77;
Δ = b2-4ac
Δ = -632-4·28·(-77)
Δ = 12593
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:

$\sqrt{\Delta}=\sqrt{12593}=\sqrt{49*257}=\sqrt{49}*\sqrt{257}=7\sqrt{257}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-7\sqrt{257}}{2*28}=\frac{63-7\sqrt{257}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+7\sqrt{257}}{2*28}=\frac{63+7\sqrt{257}}{56}
$