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4x^2+3x=5
We move all terms to the left:
4x^2+3x-(5)=0
a = 4; b = 3; c = -5;
Δ = b2-4ac
Δ = 32-4·4·(-5)
Δ = 89
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{89}}{2*4}=\frac{-3-\sqrt{89}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{89}}{2*4}=\frac{-3+\sqrt{89}}{8} $
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