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(4.20x-5.80)(7.20x-9.20)=8.00x+11.9
We move all terms to the left:
(4.20x-5.80)(7.20x-9.20)-(8.00x+11.9)=0
We add all the numbers together, and all the variables
(4.20x-5.8)(7.20x-9.2)-(8.00x+11.9)=0
We get rid of parentheses
(4.20x-5.8)(7.20x-9.2)-8.00x-11.9=0
We multiply parentheses ..
(+28x^2-36.8x-40.6x+53.36)-8.00x-11.9=0
We add all the numbers together, and all the variables
(+28x^2-36.8x-40.6x+53.36)-8x-11.9=0
We get rid of parentheses
28x^2-36.8x-40.6x-8x+53.36-11.9=0
We add all the numbers together, and all the variables
28x^2-85.4x+41.46=0
a = 28; b = -85.4; c = +41.46;
Δ = b2-4ac
Δ = -85.42-4·28·41.46
Δ = 2649.64
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{-(-85.4)-\sqrt{2649.64}}{2*28}=\frac{85.4-\sqrt{2649.64}}{56} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-85.4)+\sqrt{2649.64}}{2*28}=\frac{85.4+\sqrt{2649.64}}{56} $
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