(3a-7)(a+14)=(2a+1)

Solution for (3a-7)(a+14)=(2a+1) equation:

(3a-7)(a+14)=(2a+1)

We move all terms to the left:

(3a-7)(a+14)-((2a+1))=0

We multiply parentheses ..

(+3a^2+42a-7a-98)-((2a+1))=0


We calculate terms in parentheses: -((2a+1)), so:

(2a+1)

We get rid of parentheses

2a+1

Back to the equation:

-(2a+1)


We get rid of parentheses

3a^2+42a-7a-2a-98-1=0

We add all the numbers together, and all the variables

3a^2+33a-99=0

a = 3; b = 33; c = -99;
Δ = b2-4ac
Δ = 332-4·3·(-99)
Δ = 2277
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:

$\sqrt{\Delta}=\sqrt{2277}=\sqrt{9*253}=\sqrt{9}*\sqrt{253}=3\sqrt{253}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-3\sqrt{253}}{2*3}=\frac{-33-3\sqrt{253}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+3\sqrt{253}}{2*3}=\frac{-33+3\sqrt{253}}{6}
$