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-1.4x+9=0.09x^2-0.74+1
We move all terms to the left:
-1.4x+9-(0.09x^2-0.74+1)=0
We get rid of parentheses
-0.09x^2-1.4x+0.74-1+9=0
We add all the numbers together, and all the variables
-0.09x^2-1.4x+8.74=0
a = -0.09; b = -1.4; c = +8.74;
Δ = b2-4ac
Δ = -1.42-4·(-0.09)·8.74
Δ = 5.1064
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{-(-1.4)-\sqrt{5.1064}}{2*-0.09}=\frac{1.4-\sqrt{5.1064}}{-0.18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.4)+\sqrt{5.1064}}{2*-0.09}=\frac{1.4+\sqrt{5.1064}}{-0.18} $
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