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24=-0.375(x^2)-0.75x+30
We move all terms to the left:
24-(-0.375(x^2)-0.75x+30)=0
We get rid of parentheses
0.375x^2+0.75x-30+24=0
We add all the numbers together, and all the variables
0.375x^2+0.75x-6=0
a = 0.375; b = 0.75; c = -6;
Δ = b2-4ac
Δ = 0.752-4·0.375·(-6)
Δ = 9.5625
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{-(0.75)-\sqrt{9.5625}}{2*0.375}=\frac{-0.75-\sqrt{9.5625}}{0.75} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.75)+\sqrt{9.5625}}{2*0.375}=\frac{-0.75+\sqrt{9.5625}}{0.75} $
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