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4x^2-5x-114=0
a = 4; b = -5; c = -114;
Δ = b2-4ac
Δ = -52-4·4·(-114)
Δ = 1849
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{1849}=43$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-43}{2*4}=\frac{-38}{8} =-4+3/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+43}{2*4}=\frac{48}{8} =6 $
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