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-x(x-7)=4
We move all terms to the left:
-x(x-7)-(4)=0
We multiply parentheses
-x^2+7x-4=0
We add all the numbers together, and all the variables
-1x^2+7x-4=0
a = -1; b = 7; c = -4;
Δ = b2-4ac
Δ = 72-4·(-1)·(-4)
Δ = 33
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{-(7)-\sqrt{33}}{2*-1}=\frac{-7-\sqrt{33}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{33}}{2*-1}=\frac{-7+\sqrt{33}}{-2} $
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