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.233=(87-x)(110-x)
We move all terms to the left:
.233-((87-x)(110-x))=0
We add all the numbers together, and all the variables
-((-1x+87)(-1x+110))+.233=0
We add all the numbers together, and all the variables
-((-1x+87)(-1x+110))+0.233=0
We multiply parentheses ..
-((+x^2-110x-87x+9570))+0.233=0
We calculate terms in parentheses: -((+x^2-110x-87x+9570)), so:We get rid of parentheses
(+x^2-110x-87x+9570)
We get rid of parentheses
x^2-110x-87x+9570
We add all the numbers together, and all the variables
x^2-197x+9570
Back to the equation:
-(x^2-197x+9570)
-x^2+197x-9570+0.233=0
We add all the numbers together, and all the variables
-1x^2+197x-9569.767=0
a = -1; b = 197; c = -9569.767;
Δ = b2-4ac
Δ = 1972-4·(-1)·(-9569.767)
Δ = 529.932
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{-(197)-\sqrt{529.932}}{2*-1}=\frac{-197-\sqrt{529.932}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(197)+\sqrt{529.932}}{2*-1}=\frac{-197+\sqrt{529.932}}{-2} $
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