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5x+82=x2-3x+18
We move all terms to the left:
5x+82-(x2-3x+18)=0
We add all the numbers together, and all the variables
-(+x^2-3x+18)+5x+82=0
We get rid of parentheses
-x^2+3x+5x-18+82=0
We add all the numbers together, and all the variables
-1x^2+8x+64=0
a = -1; b = 8; c = +64;
Δ = b2-4ac
Δ = 82-4·(-1)·64
Δ = 320
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{5}}{2*-1}=\frac{-8-8\sqrt{5}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{5}}{2*-1}=\frac{-8+8\sqrt{5}}{-2} $
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