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5x=x^2-126
We move all terms to the left:
5x-(x^2-126)=0
We get rid of parentheses
-x^2+5x+126=0
We add all the numbers together, and all the variables
-1x^2+5x+126=0
a = -1; b = 5; c = +126;
Δ = b2-4ac
Δ = 52-4·(-1)·126
Δ = 529
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{529}=23$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-23}{2*-1}=\frac{-28}{-2} =+14 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+23}{2*-1}=\frac{18}{-2} =-9 $
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