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1.5x^2-20+5x=8
We move all terms to the left:
1.5x^2-20+5x-(8)=0
We add all the numbers together, and all the variables
1.5x^2+5x-28=0
a = 1.5; b = 5; c = -28;
Δ = b2-4ac
Δ = 52-4·1.5·(-28)
Δ = 193
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{193}}{2*1.5}=\frac{-5-\sqrt{193}}{3} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{193}}{2*1.5}=\frac{-5+\sqrt{193}}{3} $
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