a(4a+3)=7a

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

a(4a+3)=7a

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

4a^2-7a+3a=0

We add all the numbers together, and all the variables

4a^2-4a=0

a = 4; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·4·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*4}=\frac{0}{8}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*4}=\frac{8}{8}
=1
$