1/2(6x)=4x-9

Solution for 1/2(6x)=4x-9 equation:

1/2(6x)=4x-9

We move all terms to the left:

1/2(6x)-(4x-9)=0


Domain of the equation: 26x!=0

x!=0/26

x!=0

x∈R


We get rid of parentheses

1/26x-4x+9=0

We multiply all the terms by the denominator


-4x*26x+9*26x+1=0

Wy multiply elements

-104x^2+234x+1=0

a = -104; b = 234; c = +1;
Δ = b2-4ac
Δ = 2342-4·(-104)·1
Δ = 55172
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:

$\sqrt{\Delta}=\sqrt{55172}=\sqrt{4*13793}=\sqrt{4}*\sqrt{13793}=2\sqrt{13793}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(234)-2\sqrt{13793}}{2*-104}=\frac{-234-2\sqrt{13793}}{-208}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(234)+2\sqrt{13793}}{2*-104}=\frac{-234+2\sqrt{13793}}{-208}
$