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x=-5.4x^2-5x+7=
We move all terms to the left:
x-(-5.4x^2-5x+7)=0
We get rid of parentheses
5.4x^2+5x+x-7=0
We add all the numbers together, and all the variables
5.4x^2+6x-7=0
a = 5.4; b = 6; c = -7;
Δ = b2-4ac
Δ = 62-4·5.4·(-7)
Δ = 187.2
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{-(6)-\sqrt{187.2}}{2*5.4}=\frac{-6-\sqrt{187.2}}{10.8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+\sqrt{187.2}}{2*5.4}=\frac{-6+\sqrt{187.2}}{10.8} $
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