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

Solution for 3a(2a+3)-7(2a+3)+(2a+3)(a-1)=0 equation:

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

We multiply parentheses

6a^2+9a-14a+(2a+3)(a-1)-21=0

We multiply parentheses ..

6a^2+(+2a^2-2a+3a-3)+9a-14a-21=0

We add all the numbers together, and all the variables

6a^2+(+2a^2-2a+3a-3)-5a-21=0

We get rid of parentheses

6a^2+2a^2-2a+3a-5a-3-21=0

We add all the numbers together, and all the variables

8a^2-4a-24=0

a = 8; b = -4; c = -24;
Δ = b2-4ac
Δ = -42-4·8·(-24)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-28}{2*8}=\frac{-24}{16}
=-1+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+28}{2*8}=\frac{32}{16}
=2
$