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x^2+23x-23=180
We move all terms to the left:
x^2+23x-23-(180)=0
We add all the numbers together, and all the variables
x^2+23x-203=0
a = 1; b = 23; c = -203;
Δ = b2-4ac
Δ = 232-4·1·(-203)
Δ = 1341
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1341}=\sqrt{9*149}=\sqrt{9}*\sqrt{149}=3\sqrt{149}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-3\sqrt{149}}{2*1}=\frac{-23-3\sqrt{149}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+3\sqrt{149}}{2*1}=\frac{-23+3\sqrt{149}}{2} $
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