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

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

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

We multiply parentheses ..

(+10a^2-15a+14a-21)=0

We get rid of parentheses

10a^2-15a+14a-21=0

We add all the numbers together, and all the variables

10a^2-1a-21=0

a = 10; b = -1; c = -21;
Δ = b2-4ac
Δ = -12-4·10·(-21)
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*10}=\frac{-28}{20}
=-1+2/5
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+29}{2*10}=\frac{30}{20}
=1+1/2
$