5x+(1/2)x=45-x

Solution for 5x+(1/2)x=45-x equation:

5x+(1/2)x=45-x

We move all terms to the left:

5x+(1/2)x-(45-x)=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x+(+1/2)x-(-1x+45)=0

We multiply parentheses

x^2+5x-(-1x+45)=0

We get rid of parentheses

x^2+5x+1x-45=0

We add all the numbers together, and all the variables

x^2+6x-45=0

a = 1; b = 6; c = -45;
Δ = b2-4ac
Δ = 62-4·1·(-45)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{6}}{2*1}=\frac{-6-6\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{6}}{2*1}=\frac{-6+6\sqrt{6}}{2}
$