3a(a-7)=14-4a

Solution for 3a(a-7)=14-4a equation:

3a(a-7)=14-4a

We move all terms to the left:

3a(a-7)-(14-4a)=0

We add all the numbers together, and all the variables

3a(a-7)-(-4a+14)=0

We multiply parentheses

3a^2-21a-(-4a+14)=0

We get rid of parentheses

3a^2-21a+4a-14=0

We add all the numbers together, and all the variables

3a^2-17a-14=0

a = 3; b = -17; c = -14;
Δ = b2-4ac
Δ = -172-4·3·(-14)
Δ = 457
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{457}}{2*3}=\frac{17-\sqrt{457}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{457}}{2*3}=\frac{17+\sqrt{457}}{6}
$