7a^2-4a=3

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

7a^2-4a=3

We move all terms to the left:

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

a = 7; b = -4; c = -3;
Δ = b2-4ac
Δ = -42-4·7·(-3)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-10}{2*7}=\frac{-6}{14}
=-3/7
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+10}{2*7}=\frac{14}{14}
=1
$