3(2x+1)=7x2

Solution for 3(2x+1)=7x2 equation:

3(2x+1)=7x^2

We move all terms to the left:

3(2x+1)-(7x^2)=0

determiningTheFunctionDomain
-7x^2+3(2x+1)=0

We multiply parentheses

-7x^2+6x+3=0

a = -7; b = 6; c = +3;
Δ = b2-4ac
Δ = 62-4·(-7)·3
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{30}}{2*-7}=\frac{-6-2\sqrt{30}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{30}}{2*-7}=\frac{-6+2\sqrt{30}}{-14}
$