(7x-4)(2x+5)=0

Solution for (7x-4)(2x+5)=0 equation:

(7x-4)(2x+5)=0

We multiply parentheses ..

(+14x^2+35x-8x-20)=0

We get rid of parentheses

14x^2+35x-8x-20=0

We add all the numbers together, and all the variables

14x^2+27x-20=0

a = 14; b = 27; c = -20;
Δ = b2-4ac
Δ = 272-4·14·(-20)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-43}{2*14}=\frac{-70}{28}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+43}{2*14}=\frac{16}{28}
=4/7
$