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x+1=-3/2x+6
We move all terms to the left:
x+1-(-3/2x+6)=0
Domain of the equation: 2x+6)!=0We get rid of parentheses
x∈R
x+3/2x-6+1=0
We multiply all the terms by the denominator
x*2x-6*2x+1*2x+3=0
Wy multiply elements
2x^2-12x+2x+3=0
We add all the numbers together, and all the variables
2x^2-10x+3=0
a = 2; b = -10; c = +3;
Δ = b2-4ac
Δ = -102-4·2·3
Δ = 76
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{19}}{2*2}=\frac{10-2\sqrt{19}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{19}}{2*2}=\frac{10+2\sqrt{19}}{4} $
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