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-7.5x+4+-4.5x^2=0
We add all the numbers together, and all the variables
-4.5x^2-7.5x=0
a = -4.5; b = -7.5; c = 0;
Δ = b2-4ac
Δ = -7.52-4·(-4.5)·0
Δ = 56.25
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{-(-7.5)-\sqrt{56.25}}{2*-4.5}=\frac{7.5-\sqrt{56.25}}{-9} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7.5)+\sqrt{56.25}}{2*-4.5}=\frac{7.5+\sqrt{56.25}}{-9} $
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