6.4=(4x-9)(2x+1)

Solution for 6.4=(4x-9)(2x+1) equation:

6.4=(4x-9)(2x+1)

We move all terms to the left:

6.4-((4x-9)(2x+1))=0

We multiply parentheses ..

-((+8x^2+4x-18x-9))+6.4=0


We calculate terms in parentheses: -((+8x^2+4x-18x-9)), so:

(+8x^2+4x-18x-9)

We get rid of parentheses

8x^2+4x-18x-9

We add all the numbers together, and all the variables

8x^2-14x-9

Back to the equation:

-(8x^2-14x-9)


We get rid of parentheses

-8x^2+14x+9+6.4=0

We add all the numbers together, and all the variables

-8x^2+14x+15.4=0

a = -8; b = 14; c = +15.4;
Δ = b2-4ac
Δ = 142-4·(-8)·15.4
Δ = 688.8
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{-(14)-\sqrt{688.8}}{2*-8}=\frac{-14-\sqrt{688.8}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+\sqrt{688.8}}{2*-8}=\frac{-14+\sqrt{688.8}}{-16}
$