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

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

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

We multiply parentheses ..

(+10a^2-6a+35a-21)=0

We get rid of parentheses

10a^2-6a+35a-21=0

We add all the numbers together, and all the variables

10a^2+29a-21=0

a = 10; b = 29; c = -21;
Δ = b2-4ac
Δ = 292-4·10·(-21)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-41}{2*10}=\frac{-70}{20}
=-3+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+41}{2*10}=\frac{12}{20}
=3/5
$