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4x^2+5x-39/16=0
We multiply all the terms by the denominator
4x^2*16+5x*16-39=0
Wy multiply elements
64x^2+80x-39=0
a = 64; b = 80; c = -39;
Δ = b2-4ac
Δ = 802-4·64·(-39)
Δ = 16384
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{16384}=128$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-128}{2*64}=\frac{-208}{128} =-1+5/8 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+128}{2*64}=\frac{48}{128} =3/8 $
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