4x-5=0.75(8x-4)4x-5=0.75(8x-4)4x-5=0.75(8x-4)4x-5=0.75(8x-4)4x-5=0.75(8x-4)

Solution for 4x-5=0.75(8x-4)4x-5=0.75(8x-4)4x-5=0.75(8x-4)4x-5=0.75(8x-4)4x-5=0.75(8x-4) equation:

4x-5=0.75(8x-4)4x-5=0.75(8x-4)4x-5=0.75(8x-4)4x-5=0.75(8x-4)4x-5=0.75(8x-4)

We move all terms to the left:

4x-5-(0.75(8x-4)4x-5)=0


We calculate terms in parentheses: -(0.75(8x-4)4x-5), so:

0.75(8x-4)4x-5

We multiply parentheses

24x^2-12x-5

Back to the equation:

-(24x^2-12x-5)


We get rid of parentheses

-24x^2+4x+12x+5-5=0

We add all the numbers together, and all the variables

-24x^2+16x=0

a = -24; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-24)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-24}=\frac{-32}{-48}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-24}=\frac{0}{-48}
=0
$