1-3x*7=9x^2-3

Solution for 1-3x*7=9x^2-3 equation:

1-3x*7=9x^2-3

We move all terms to the left:

1-3x*7-(9x^2-3)=0

Wy multiply elements

-21x-(9x^2-3)+1=0

We get rid of parentheses

-9x^2-21x+3+1=0

We add all the numbers together, and all the variables

-9x^2-21x+4=0

a = -9; b = -21; c = +4;
Δ = b2-4ac
Δ = -212-4·(-9)·4
Δ = 585
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:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{65}}{2*-9}=\frac{21-3\sqrt{65}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{65}}{2*-9}=\frac{21+3\sqrt{65}}{-18}
$