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x(x-2)=4x+7
We move all terms to the left:
x(x-2)-(4x+7)=0
We multiply parentheses
x^2-2x-(4x+7)=0
We get rid of parentheses
x^2-2x-4x-7=0
We add all the numbers together, and all the variables
x^2-6x-7=0
a = 1; b = -6; c = -7;
Δ = b2-4ac
Δ = -62-4·1·(-7)
Δ = 64
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{64}=8$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-8}{2*1}=\frac{-2}{2} =-1 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+8}{2*1}=\frac{14}{2} =7 $
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