4a(a-1)+3=7

Solution for 4a(a-1)+3=7 equation:

4a(a-1)+3=7

We move all terms to the left:

4a(a-1)+3-(7)=0

We add all the numbers together, and all the variables

4a(a-1)-4=0

We multiply parentheses

4a^2-4a-4=0

a = 4; b = -4; c = -4;
Δ = b2-4ac
Δ = -42-4·4·(-4)
Δ = 80
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{5}}{2*4}=\frac{4-4\sqrt{5}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{5}}{2*4}=\frac{4+4\sqrt{5}}{8}
$