(10x-7)(4x+5)=0

Solution for (10x-7)(4x+5)=0 equation:

(10x-7)(4x+5)=0

We multiply parentheses ..

(+40x^2+50x-28x-35)=0

We get rid of parentheses

40x^2+50x-28x-35=0

We add all the numbers together, and all the variables

40x^2+22x-35=0

a = 40; b = 22; c = -35;
Δ = b2-4ac
Δ = 222-4·40·(-35)
Δ = 6084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6084}=78$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-78}{2*40}=\frac{-100}{80}
=-1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+78}{2*40}=\frac{56}{80}
=7/10
$