7x(x+1)=3/9

Solution for 7x(x+1)=3/9 equation:

7x(x+1)=3/9

We move all terms to the left:

7x(x+1)-(3/9)=0

We add all the numbers together, and all the variables

7x(x+1)-(+3/9)=0

We multiply parentheses

7x^2+7x-(+3/9)=0

We get rid of parentheses

7x^2+7x-3/9=0

We multiply all the terms by the denominator


7x^2*9+7x*9-3=0

Wy multiply elements

63x^2+63x-3=0

a = 63; b = 63; c = -3;
Δ = b2-4ac
Δ = 632-4·63·(-3)
Δ = 4725
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:

$\sqrt{\Delta}=\sqrt{4725}=\sqrt{225*21}=\sqrt{225}*\sqrt{21}=15\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-15\sqrt{21}}{2*63}=\frac{-63-15\sqrt{21}}{126}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+15\sqrt{21}}{2*63}=\frac{-63+15\sqrt{21}}{126}
$