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6x^2+9x=60
We move all terms to the left:
6x^2+9x-(60)=0
a = 6; b = 9; c = -60;
Δ = b2-4ac
Δ = 92-4·6·(-60)
Δ = 1521
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{1521}=39$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-39}{2*6}=\frac{-48}{12} =-4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+39}{2*6}=\frac{30}{12} =2+1/2 $
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