x+45=1/2x+12

Solution for x+45=1/2x+12 equation:

x+45=1/2x+12

We move all terms to the left:

x+45-(1/2x+12)=0


Domain of the equation: 2x+12)!=0

x∈R


We get rid of parentheses

x-1/2x-12+45=0

We multiply all the terms by the denominator


x*2x-12*2x+45*2x-1=0

Wy multiply elements

2x^2-24x+90x-1=0

We add all the numbers together, and all the variables

2x^2+66x-1=0

a = 2; b = 66; c = -1;
Δ = b2-4ac
Δ = 662-4·2·(-1)
Δ = 4364
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:

$\sqrt{\Delta}=\sqrt{4364}=\sqrt{4*1091}=\sqrt{4}*\sqrt{1091}=2\sqrt{1091}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-2\sqrt{1091}}{2*2}=\frac{-66-2\sqrt{1091}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+2\sqrt{1091}}{2*2}=\frac{-66+2\sqrt{1091}}{4}
$