7a(3+2a)=25-7

Solution for 7a(3+2a)=25-7 equation:

7a(3+2a)=25-7

We move all terms to the left:

7a(3+2a)-(25-7)=0

We add all the numbers together, and all the variables

7a(2a+3)-18=0

We multiply parentheses

14a^2+21a-18=0

a = 14; b = 21; c = -18;
Δ = b2-4ac
Δ = 212-4·14·(-18)
Δ = 1449
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:

$\sqrt{\Delta}=\sqrt{1449}=\sqrt{9*161}=\sqrt{9}*\sqrt{161}=3\sqrt{161}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{161}}{2*14}=\frac{-21-3\sqrt{161}}{28}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{161}}{2*14}=\frac{-21+3\sqrt{161}}{28}
$