(5x-7)(8x+3)=0

Solution for (5x-7)(8x+3)=0 equation:

(5x-7)(8x+3)=0

We multiply parentheses ..

(+40x^2+15x-56x-21)=0

We get rid of parentheses

40x^2+15x-56x-21=0

We add all the numbers together, and all the variables

40x^2-41x-21=0

a = 40; b = -41; c = -21;
Δ = b2-4ac
Δ = -412-4·40·(-21)
Δ = 5041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5041}=71$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-71}{2*40}=\frac{-30}{80}
=-3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+71}{2*40}=\frac{112}{80}
=1+2/5
$