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4x(116+x)+x+2(116+x)+116=4x-116+x
We move all terms to the left:
4x(116+x)+x+2(116+x)+116-(4x-116+x)=0
We add all the numbers together, and all the variables
4x(x+116)+x+2(x+116)-(5x-116)+116=0
We add all the numbers together, and all the variables
x+4x(x+116)+2(x+116)-(5x-116)+116=0
We multiply parentheses
4x^2+x+464x+2x-(5x-116)+232+116=0
We get rid of parentheses
4x^2+x+464x+2x-5x+116+232+116=0
We add all the numbers together, and all the variables
4x^2+462x+464=0
a = 4; b = 462; c = +464;
Δ = b2-4ac
Δ = 4622-4·4·464
Δ = 206020
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{206020}=\sqrt{4*51505}=\sqrt{4}*\sqrt{51505}=2\sqrt{51505}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(462)-2\sqrt{51505}}{2*4}=\frac{-462-2\sqrt{51505}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(462)+2\sqrt{51505}}{2*4}=\frac{-462+2\sqrt{51505}}{8} $
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