(4x-5)(7x+3)=0

Solution for (4x-5)(7x+3)=0 equation:

(4x-5)(7x+3)=0

We multiply parentheses ..

(+28x^2+12x-35x-15)=0

We get rid of parentheses

28x^2+12x-35x-15=0

We add all the numbers together, and all the variables

28x^2-23x-15=0

a = 28; b = -23; c = -15;
Δ = b2-4ac
Δ = -232-4·28·(-15)
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-47}{2*28}=\frac{-24}{56}
=-3/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+47}{2*28}=\frac{70}{56}
=1+1/4
$