7x(x+1)=3

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

7x(x+1)=3

We move all terms to the left:

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

We multiply parentheses

7x^2+7x-3=0

a = 7; b = 7; c = -3;
Δ = b2-4ac
Δ = 72-4·7·(-3)
Δ = 133
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{-(7)-\sqrt{133}}{2*7}=\frac{-7-\sqrt{133}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{133}}{2*7}=\frac{-7+\sqrt{133}}{14}
$