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(4.20x-5.80)(7.20x-9.20)=10.0x+9.10
We move all terms to the left:
(4.20x-5.80)(7.20x-9.20)-(10.0x+9.10)=0
We add all the numbers together, and all the variables
(4.20x-5.8)(7.20x-9.2)-(10.0x+9.1)=0
We get rid of parentheses
(4.20x-5.8)(7.20x-9.2)-10.0x-9.1=0
We multiply parentheses ..
(+28x^2-36.8x-40.6x+53.36)-10.0x-9.1=0
We add all the numbers together, and all the variables
(+28x^2-36.8x-40.6x+53.36)-10x-9.1=0
We get rid of parentheses
28x^2-36.8x-40.6x-10x+53.36-9.1=0
We add all the numbers together, and all the variables
28x^2-87.4x+44.26=0
a = 28; b = -87.4; c = +44.26;
Δ = b2-4ac
Δ = -87.42-4·28·44.26
Δ = 2681.64
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{-(-87.4)-\sqrt{2681.64}}{2*28}=\frac{87.4-\sqrt{2681.64}}{56} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-87.4)+\sqrt{2681.64}}{2*28}=\frac{87.4+\sqrt{2681.64}}{56} $
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