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1/2x+3=2x-15
We move all terms to the left:
1/2x+3-(2x-15)=0
Domain of the equation: 2x!=0We get rid of parentheses
x!=0/2
x!=0
x∈R
1/2x-2x+15+3=0
We multiply all the terms by the denominator
-2x*2x+15*2x+3*2x+1=0
Wy multiply elements
-4x^2+30x+6x+1=0
We add all the numbers together, and all the variables
-4x^2+36x+1=0
a = -4; b = 36; c = +1;
Δ = b2-4ac
Δ = 362-4·(-4)·1
Δ = 1312
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1312}=\sqrt{16*82}=\sqrt{16}*\sqrt{82}=4\sqrt{82}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{82}}{2*-4}=\frac{-36-4\sqrt{82}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{82}}{2*-4}=\frac{-36+4\sqrt{82}}{-8} $
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