-3x^2+1=7x

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

-3x^2+1=7x

We move all terms to the left:

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

a = -3; b = -7; c = +1;
Δ = b2-4ac
Δ = -72-4·(-3)·1
Δ = 61
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{61}}{2*-3}=\frac{7-\sqrt{61}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{61}}{2*-3}=\frac{7+\sqrt{61}}{-6}
$