(3a+7)(2a-5)=0

Solution for (3a+7)(2a-5)=0 equation:

(3a+7)(2a-5)=0

We multiply parentheses ..

(+6a^2-15a+14a-35)=0

We get rid of parentheses

6a^2-15a+14a-35=0

We add all the numbers together, and all the variables

6a^2-1a-35=0

a = 6; b = -1; c = -35;
Δ = b2-4ac
Δ = -12-4·6·(-35)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-29}{2*6}=\frac{-28}{12}
=-2+1/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+29}{2*6}=\frac{30}{12}
=2+1/2
$