2.5=X(2x-6)

Solution for 2.5=X(2x-6) equation:

2.5=X(2X-6)

We move all terms to the left:

2.5-(X(2X-6))=0


We calculate terms in parentheses: -(X(2X-6)), so:

X(2X-6)

We multiply parentheses

2X^2-6X

Back to the equation:

-(2X^2-6X)


We get rid of parentheses

-2X^2+6X+2.5=0

a = -2; b = 6; c = +2.5;
Δ = b2-4ac
Δ = 62-4·(-2)·2.5
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{14}}{2*-2}=\frac{-6-2\sqrt{14}}{-4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{14}}{2*-2}=\frac{-6+2\sqrt{14}}{-4}
$