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(5x+82)+(x^2-3x+18)=180
We move all terms to the left:
(5x+82)+(x^2-3x+18)-(180)=0
We get rid of parentheses
x^2+5x-3x+82+18-180=0
We add all the numbers together, and all the variables
x^2+2x-80=0
a = 1; b = 2; c = -80;
Δ = b2-4ac
Δ = 22-4·1·(-80)
Δ = 324
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{324}=18$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-18}{2*1}=\frac{-20}{2} =-10 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+18}{2*1}=\frac{16}{2} =8 $
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