1/2xx4=3x+45

Solution for 1/2xx4=3x+45 equation:

1/2xx4=3x+45

We move all terms to the left:

1/2xx4-(3x+45)=0


Domain of the equation: 2xx4!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

1/2xx4-3x-45=0

We multiply all the terms by the denominator


-3x*2xx4-45*2xx4+1=0

Wy multiply elements

-6x^2-90x+1=0

a = -6; b = -90; c = +1;
Δ = b2-4ac
Δ = -902-4·(-6)·1
Δ = 8124
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:

$\sqrt{\Delta}=\sqrt{8124}=\sqrt{4*2031}=\sqrt{4}*\sqrt{2031}=2\sqrt{2031}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{2031}}{2*-6}=\frac{90-2\sqrt{2031}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{2031}}{2*-6}=\frac{90+2\sqrt{2031}}{-12}
$