7x2-1=3x

Solution for 7x2-1=3x equation:

7x^2-1=3x

We move all terms to the left:

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

a = 7; b = -3; c = -1;
Δ = b2-4ac
Δ = -32-4·7·(-1)
Δ = 37
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{-(-3)-\sqrt{37}}{2*7}=\frac{3-\sqrt{37}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{37}}{2*7}=\frac{3+\sqrt{37}}{14}
$