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4x^2+6x+3/2=0
We multiply all the terms by the denominator
4x^2*2+6x*2+3=0
Wy multiply elements
8x^2+12x+3=0
a = 8; b = 12; c = +3;
Δ = b2-4ac
Δ = 122-4·8·3
Δ = 48
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{3}}{2*8}=\frac{-12-4\sqrt{3}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{3}}{2*8}=\frac{-12+4\sqrt{3}}{16} $
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