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x(2x+5)=108
We move all terms to the left:
x(2x+5)-(108)=0
We multiply parentheses
2x^2+5x-108=0
a = 2; b = 5; c = -108;
Δ = b2-4ac
Δ = 52-4·2·(-108)
Δ = 889
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{889}}{2*2}=\frac{-5-\sqrt{889}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{889}}{2*2}=\frac{-5+\sqrt{889}}{4} $
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