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

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

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

We multiply parentheses ..

(+20x^2+16x+35x+28)=0

We get rid of parentheses

20x^2+16x+35x+28=0

We add all the numbers together, and all the variables

20x^2+51x+28=0

a = 20; b = 51; c = +28;
Δ = b2-4ac
Δ = 512-4·20·28
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-19}{2*20}=\frac{-70}{40}
=-1+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+19}{2*20}=\frac{-32}{40}
=-4/5
$