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-x^2+18x=70
We move all terms to the left:
-x^2+18x-(70)=0
We add all the numbers together, and all the variables
-1x^2+18x-70=0
a = -1; b = 18; c = -70;
Δ = b2-4ac
Δ = 182-4·(-1)·(-70)
Δ = 44
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{11}}{2*-1}=\frac{-18-2\sqrt{11}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{11}}{2*-1}=\frac{-18+2\sqrt{11}}{-2} $
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