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7.5-0.3x=0.75(x2)-1.5
We move all terms to the left:
7.5-0.3x-(0.75(x2)-1.5)=0
We add all the numbers together, and all the variables
-(+0.75x^2-1.5)-0.3x+7.5=0
We get rid of parentheses
-0.75x^2-0.3x+1.5+7.5=0
We add all the numbers together, and all the variables
-0.75x^2-0.3x+9=0
a = -0.75; b = -0.3; c = +9;
Δ = b2-4ac
Δ = -0.32-4·(-0.75)·9
Δ = 27.09
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{-(-0.3)-\sqrt{27.09}}{2*-0.75}=\frac{0.3-\sqrt{27.09}}{-1.5} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.3)+\sqrt{27.09}}{2*-0.75}=\frac{0.3+\sqrt{27.09}}{-1.5} $
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