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

Solution for 6.5(x+4)=7(x-2)x= equation:

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

We move all terms to the left:

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

We multiply parentheses

6.5x-(7(x-2)x)+26=0


We calculate terms in parentheses: -(7(x-2)x), so:

7(x-2)x

We multiply parentheses

7x^2-14x

Back to the equation:

-(7x^2-14x)


We get rid of parentheses

-7x^2+6.5x+14x+26=0

We add all the numbers together, and all the variables

-7x^2+20.5x+26=0

a = -7; b = 20.5; c = +26;
Δ = b2-4ac
Δ = 20.52-4·(-7)·26
Δ = 1148.25
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{-(20.5)-\sqrt{1148.25}}{2*-7}=\frac{-20.5-\sqrt{1148.25}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20.5)+\sqrt{1148.25}}{2*-7}=\frac{-20.5+\sqrt{1148.25}}{-14}
$