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x^2+2x=3/2
We move all terms to the left:
x^2+2x-(3/2)=0
We add all the numbers together, and all the variables
x^2+2x-(+3/2)=0
We get rid of parentheses
x^2+2x-3/2=0
We multiply all the terms by the denominator
x^2*2+2x*2-3=0
Wy multiply elements
2x^2+4x-3=0
a = 2; b = 4; c = -3;
Δ = b2-4ac
Δ = 42-4·2·(-3)
Δ = 40
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{10}}{2*2}=\frac{-4-2\sqrt{10}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{10}}{2*2}=\frac{-4+2\sqrt{10}}{4} $
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