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4x+x2+21=180
We move all terms to the left:
4x+x2+21-(180)=0
We add all the numbers together, and all the variables
x^2+4x-159=0
a = 1; b = 4; c = -159;
Δ = b2-4ac
Δ = 42-4·1·(-159)
Δ = 652
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{652}=\sqrt{4*163}=\sqrt{4}*\sqrt{163}=2\sqrt{163}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{163}}{2*1}=\frac{-4-2\sqrt{163}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{163}}{2*1}=\frac{-4+2\sqrt{163}}{2} $
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