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x^2-3x-5/4=0
We multiply all the terms by the denominator
x^2*4-3x*4-5=0
Wy multiply elements
4x^2-12x-5=0
a = 4; b = -12; c = -5;
Δ = b2-4ac
Δ = -122-4·4·(-5)
Δ = 224
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{14}}{2*4}=\frac{12-4\sqrt{14}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{14}}{2*4}=\frac{12+4\sqrt{14}}{8} $
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