7x^2-4=3x

Solution for 7x^2-4=3x equation:

7x^2-4=3x

We move all terms to the left:

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

a = 7; b = -3; c = -4;
Δ = b2-4ac
Δ = -32-4·7·(-4)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-11}{2*7}=\frac{-8}{14}
=-4/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+11}{2*7}=\frac{14}{14}
=1
$