(4x-1)(x+3)=5x(0.8x+2)

Solution for (4x-1)(x+3)=5x(0.8x+2) equation:

(4x-1)(x+3)=5x(0.8x+2)

We move all terms to the left:

(4x-1)(x+3)-(5x(0.8x+2))=0

We multiply parentheses ..

(+4x^2+12x-1x-3)-(5x(0.8x+2))=0


We calculate terms in parentheses: -(5x(0.8x+2)), so:

5x(0.8x+2)

We multiply parentheses

0x^2+10x

We add all the numbers together, and all the variables

x^2+10x

Back to the equation:

-(x^2+10x)


We get rid of parentheses

4x^2-x^2+12x-1x-10x-3=0

We add all the numbers together, and all the variables

3x^2+x-3=0

a = 3; b = 1; c = -3;
Δ = b2-4ac
Δ = 12-4·3·(-3)
Δ = 37
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{37}}{2*3}=\frac{-1-\sqrt{37}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{37}}{2*3}=\frac{-1+\sqrt{37}}{6}
$