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

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

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

We multiply parentheses ..

(+4x^2-20x-7x+35)=0

We get rid of parentheses

4x^2-20x-7x+35=0

We add all the numbers together, and all the variables

4x^2-27x+35=0

a = 4; b = -27; c = +35;
Δ = b2-4ac
Δ = -272-4·4·35
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-13}{2*4}=\frac{14}{8}
=1+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+13}{2*4}=\frac{40}{8}
=5
$