4n^2-7n=3=0

Solution for 4n^2-7n=3=0 equation:

4n^2-7n=3=0

We move all terms to the left:

4n^2-7n-(3)=0

a = 4; b = -7; c = -3;
Δ = b2-4ac
Δ = -72-4·4·(-3)
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{97}}{2*4}=\frac{7-\sqrt{97}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{97}}{2*4}=\frac{7+\sqrt{97}}{8}
$