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5x^2+7x=11
We move all terms to the left:
5x^2+7x-(11)=0
a = 5; b = 7; c = -11;
Δ = b2-4ac
Δ = 72-4·5·(-11)
Δ = 269
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{269}}{2*5}=\frac{-7-\sqrt{269}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{269}}{2*5}=\frac{-7+\sqrt{269}}{10} $
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