(a-5)*(2a-7)=0

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

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

We multiply parentheses ..

(+2a^2-7a-10a+35)=0

We get rid of parentheses

2a^2-7a-10a+35=0

We add all the numbers together, and all the variables

2a^2-17a+35=0

a = 2; b = -17; c = +35;
Δ = b2-4ac
Δ = -172-4·2·35
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-3}{2*2}=\frac{14}{4}
=3+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+3}{2*2}=\frac{20}{4}
=5
$