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5x^2=-3x-1/4
We move all terms to the left:
5x^2-(-3x-1/4)=0
We get rid of parentheses
5x^2+3x+1/4=0
We multiply all the terms by the denominator
5x^2*4+3x*4+1=0
Wy multiply elements
20x^2+12x+1=0
a = 20; b = 12; c = +1;
Δ = b2-4ac
Δ = 122-4·20·1
Δ = 64
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{64}=8$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8}{2*20}=\frac{-20}{40} =-1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8}{2*20}=\frac{-4}{40} =-1/10 $
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