3x(x+1)=7

Solution for 3x(x+1)=7 equation:

3x(x+1)=7

We move all terms to the left:

3x(x+1)-(7)=0

We multiply parentheses

3x^2+3x-7=0

a = 3; b = 3; c = -7;
Δ = b2-4ac
Δ = 32-4·3·(-7)
Δ = 93
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{93}}{2*3}=\frac{-3-\sqrt{93}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{93}}{2*3}=\frac{-3+\sqrt{93}}{6}
$