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X^2+3X+20X+3=180
We move all terms to the left:
X^2+3X+20X+3-(180)=0
We add all the numbers together, and all the variables
X^2+23X-177=0
a = 1; b = 23; c = -177;
Δ = b2-4ac
Δ = 232-4·1·(-177)
Δ = 1237
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-\sqrt{1237}}{2*1}=\frac{-23-\sqrt{1237}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{1237}}{2*1}=\frac{-23+\sqrt{1237}}{2} $
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