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18+3x-5=7x(-14-x)
We move all terms to the left:
18+3x-5-(7x(-14-x))=0
We add all the numbers together, and all the variables
3x-(7x(-1x-14))+18-5=0
We add all the numbers together, and all the variables
3x-(7x(-1x-14))+13=0
We calculate terms in parentheses: -(7x(-1x-14)), so:We get rid of parentheses
7x(-1x-14)
We multiply parentheses
-7x^2-98x
Back to the equation:
-(-7x^2-98x)
7x^2+98x+3x+13=0
We add all the numbers together, and all the variables
7x^2+101x+13=0
a = 7; b = 101; c = +13;
Δ = b2-4ac
Δ = 1012-4·7·13
Δ = 9837
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9837}=\sqrt{9*1093}=\sqrt{9}*\sqrt{1093}=3\sqrt{1093}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(101)-3\sqrt{1093}}{2*7}=\frac{-101-3\sqrt{1093}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(101)+3\sqrt{1093}}{2*7}=\frac{-101+3\sqrt{1093}}{14} $
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