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5x^2+5x-54=6
We move all terms to the left:
5x^2+5x-54-(6)=0
We add all the numbers together, and all the variables
5x^2+5x-60=0
a = 5; b = 5; c = -60;
Δ = b2-4ac
Δ = 52-4·5·(-60)
Δ = 1225
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{1225}=35$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-35}{2*5}=\frac{-40}{10} =-4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+35}{2*5}=\frac{30}{10} =3 $
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