7x-5(x-4)=4x(x+2)

Solution for 7x-5(x-4)=4x(x+2) equation:

7x-5(x-4)=4x(x+2)

We move all terms to the left:

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

We multiply parentheses

7x-5x-(4x(x+2))+20=0


We calculate terms in parentheses: -(4x(x+2)), so:

4x(x+2)

We multiply parentheses

4x^2+8x

Back to the equation:

-(4x^2+8x)


We add all the numbers together, and all the variables

2x-(4x^2+8x)+20=0

We get rid of parentheses

-4x^2+2x-8x+20=0

We add all the numbers together, and all the variables

-4x^2-6x+20=0

a = -4; b = -6; c = +20;
Δ = b2-4ac
Δ = -62-4·(-4)·20
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{89}}{2*-4}=\frac{6-2\sqrt{89}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{89}}{2*-4}=\frac{6+2\sqrt{89}}{-8}
$