7(6-2a)=4a(2a+4)

Solution for 7(6-2a)=4a(2a+4) equation:

7(6-2a)=4a(2a+4)

We move all terms to the left:

7(6-2a)-(4a(2a+4))=0

We add all the numbers together, and all the variables

7(-2a+6)-(4a(2a+4))=0

We multiply parentheses

-14a-(4a(2a+4))+42=0


We calculate terms in parentheses: -(4a(2a+4)), so:

4a(2a+4)

We multiply parentheses

8a^2+16a

Back to the equation:

-(8a^2+16a)


We get rid of parentheses

-8a^2-14a-16a+42=0

We add all the numbers together, and all the variables

-8a^2-30a+42=0

a = -8; b = -30; c = +42;
Δ = b2-4ac
Δ = -302-4·(-8)·42
Δ = 2244
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:

$\sqrt{\Delta}=\sqrt{2244}=\sqrt{4*561}=\sqrt{4}*\sqrt{561}=2\sqrt{561}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{561}}{2*-8}=\frac{30-2\sqrt{561}}{-16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{561}}{2*-8}=\frac{30+2\sqrt{561}}{-16}
$