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5x^2+5x-1/2=0
We multiply all the terms by the denominator
5x^2*2+5x*2-1=0
Wy multiply elements
10x^2+10x-1=0
a = 10; b = 10; c = -1;
Δ = b2-4ac
Δ = 102-4·10·(-1)
Δ = 140
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{35}}{2*10}=\frac{-10-2\sqrt{35}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{35}}{2*10}=\frac{-10+2\sqrt{35}}{20} $
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