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2x-9=-3/2x+5
We move all terms to the left:
2x-9-(-3/2x+5)=0
Domain of the equation: 2x+5)!=0We get rid of parentheses
x∈R
2x+3/2x-5-9=0
We multiply all the terms by the denominator
2x*2x-5*2x-9*2x+3=0
Wy multiply elements
4x^2-10x-18x+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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