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5x^2-7x-3=0
a = 5; b = -7; c = -3;
Δ = b2-4ac
Δ = -72-4·5·(-3)
Δ = 109
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{-(-7)-\sqrt{109}}{2*5}=\frac{7-\sqrt{109}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{109}}{2*5}=\frac{7+\sqrt{109}}{10} $
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