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5x^2+7x=66
We move all terms to the left:
5x^2+7x-(66)=0
a = 5; b = 7; c = -66;
Δ = b2-4ac
Δ = 72-4·5·(-66)
Δ = 1369
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{1369}=37$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-37}{2*5}=\frac{-44}{10} =-4+2/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+37}{2*5}=\frac{30}{10} =3 $
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