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

Solution for x^2+x+3=7x^2-3 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-6x^2+x+6=0

a = -6; b = 1; c = +6;
Δ = b2-4ac
Δ = 12-4·(-6)·6
Δ = 145
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{-(1)-\sqrt{145}}{2*-6}=\frac{-1-\sqrt{145}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{145}}{2*-6}=\frac{-1+\sqrt{145}}{-12}
$