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3/2x+5=5-2x+-14
We move all terms to the left:
3/2x+5-(5-2x+-14)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
3/2x-(-2x-9)+5=0
We get rid of parentheses
3/2x+2x+9+5=0
We multiply all the terms by the denominator
2x*2x+9*2x+5*2x+3=0
Wy multiply elements
4x^2+18x+10x+3=0
We add all the numbers together, and all the variables
4x^2+28x+3=0
a = 4; b = 28; c = +3;
Δ = b2-4ac
Δ = 282-4·4·3
Δ = 736
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{46}}{2*4}=\frac{-28-4\sqrt{46}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{46}}{2*4}=\frac{-28+4\sqrt{46}}{8} $
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