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1.5x^2+5x=92
We move all terms to the left:
1.5x^2+5x-(92)=0
a = 1.5; b = 5; c = -92;
Δ = b2-4ac
Δ = 52-4·1.5·(-92)
Δ = 577
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{577}}{2*1.5}=\frac{-5-\sqrt{577}}{3} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{577}}{2*1.5}=\frac{-5+\sqrt{577}}{3} $
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