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8x+21+x2=180
We move all terms to the left:
8x+21+x2-(180)=0
We add all the numbers together, and all the variables
x^2+8x-159=0
a = 1; b = 8; c = -159;
Δ = b2-4ac
Δ = 82-4·1·(-159)
Δ = 700
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-10\sqrt{7}}{2*1}=\frac{-8-10\sqrt{7}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+10\sqrt{7}}{2*1}=\frac{-8+10\sqrt{7}}{2} $
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