7x^2-x=3

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

7x^2-x=3

We move all terms to the left:

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

We add all the numbers together, and all the variables

7x^2-1x-3=0

a = 7; b = -1; c = -3;
Δ = b2-4ac
Δ = -12-4·7·(-3)
Δ = 85
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{85}}{2*7}=\frac{1-\sqrt{85}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{85}}{2*7}=\frac{1+\sqrt{85}}{14}
$