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

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

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

We move all terms to the left:

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

We multiply parentheses

7x^2-28x-(4x+5)=0

We get rid of parentheses

7x^2-28x-4x-5=0

We add all the numbers together, and all the variables

7x^2-32x-5=0

a = 7; b = -32; c = -5;
Δ = b2-4ac
Δ = -322-4·7·(-5)
Δ = 1164
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1164}=\sqrt{4*291}=\sqrt{4}*\sqrt{291}=2\sqrt{291}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{291}}{2*7}=\frac{32-2\sqrt{291}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{291}}{2*7}=\frac{32+2\sqrt{291}}{14}
$