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1.5=-1.875x^2+7.5x
We move all terms to the left:
1.5-(-1.875x^2+7.5x)=0
We get rid of parentheses
1.875x^2-7.5x+1.5=0
a = 1.875; b = -7.5; c = +1.5;
Δ = b2-4ac
Δ = -7.52-4·1.875·1.5
Δ = 45
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7.5)-3\sqrt{5}}{2*1.875}=\frac{7.5-3\sqrt{5}}{3.75} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7.5)+3\sqrt{5}}{2*1.875}=\frac{7.5+3\sqrt{5}}{3.75} $
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