4(5x-4)(x-1)=3(4)(x+1)

Solution for 4(5x-4)(x-1)=3(4)(x+1) equation:

4(5x-4)(x-1)=3(4)(x+1)

We move all terms to the left:

4(5x-4)(x-1)-(3(4)(x+1))=0

We multiply parentheses ..

4(+5x^2-5x-4x+4)-(34(x+1))=0


We calculate terms in parentheses: -(34(x+1)), so:

34(x+1)

We multiply parentheses

34x+34

Back to the equation:

-(34x+34)


We multiply parentheses

20x^2-20x-16x-(34x+34)+16=0

We get rid of parentheses

20x^2-20x-16x-34x-34+16=0

We add all the numbers together, and all the variables

20x^2-70x-18=0

a = 20; b = -70; c = -18;
Δ = b2-4ac
Δ = -702-4·20·(-18)
Δ = 6340
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:

$\sqrt{\Delta}=\sqrt{6340}=\sqrt{4*1585}=\sqrt{4}*\sqrt{1585}=2\sqrt{1585}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-2\sqrt{1585}}{2*20}=\frac{70-2\sqrt{1585}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+2\sqrt{1585}}{2*20}=\frac{70+2\sqrt{1585}}{40}
$