3x(x+10)=77

Solution for 3x(x+10)=77 equation:

3x(x+10)=77

We move all terms to the left:

3x(x+10)-(77)=0

We multiply parentheses

3x^2+30x-77=0

a = 3; b = 30; c = -77;
Δ = b2-4ac
Δ = 302-4·3·(-77)
Δ = 1824
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:

$\sqrt{\Delta}=\sqrt{1824}=\sqrt{16*114}=\sqrt{16}*\sqrt{114}=4\sqrt{114}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-4\sqrt{114}}{2*3}=\frac{-30-4\sqrt{114}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+4\sqrt{114}}{2*3}=\frac{-30+4\sqrt{114}}{6}
$