(5b-2)(8b-7)=0

Solution for (5b-2)(8b-7)=0 equation:

(5b-2)(8b-7)=0

We multiply parentheses ..

(+40b^2-35b-16b+14)=0

We get rid of parentheses

40b^2-35b-16b+14=0

We add all the numbers together, and all the variables

40b^2-51b+14=0

a = 40; b = -51; c = +14;
Δ = b2-4ac
Δ = -512-4·40·14
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-19}{2*40}=\frac{32}{80}
=2/5
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+19}{2*40}=\frac{70}{80}
=7/8
$