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x(x-6)=5x-24
We move all terms to the left:
x(x-6)-(5x-24)=0
We multiply parentheses
x^2-6x-(5x-24)=0
We get rid of parentheses
x^2-6x-5x+24=0
We add all the numbers together, and all the variables
x^2-11x+24=0
a = 1; b = -11; c = +24;
Δ = b2-4ac
Δ = -112-4·1·24
Δ = 25
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{25}=5$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-5}{2*1}=\frac{6}{2} =3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+5}{2*1}=\frac{16}{2} =8 $
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