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5x(x+1)=6
We move all terms to the left:
5x(x+1)-(6)=0
We multiply parentheses
5x^2+5x-6=0
a = 5; b = 5; c = -6;
Δ = b2-4ac
Δ = 52-4·5·(-6)
Δ = 145
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{-(5)-\sqrt{145}}{2*5}=\frac{-5-\sqrt{145}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{145}}{2*5}=\frac{-5+\sqrt{145}}{10} $
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