5(4x-7)(3x-8)=0

Solution for 5(4x-7)(3x-8)=0 equation:

5(4x-7)(3x-8)=0

We multiply parentheses ..

5(+12x^2-32x-21x+56)=0

We multiply parentheses

60x^2-160x-105x+280=0

We add all the numbers together, and all the variables

60x^2-265x+280=0

a = 60; b = -265; c = +280;
Δ = b2-4ac
Δ = -2652-4·60·280
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-265)-55}{2*60}=\frac{210}{120}
=1+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-265)+55}{2*60}=\frac{320}{120}
=2+2/3
$