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6x-2x(x-5)=22
We move all terms to the left:
6x-2x(x-5)-(22)=0
We multiply parentheses
-2x^2+6x+10x-22=0
We add all the numbers together, and all the variables
-2x^2+16x-22=0
a = -2; b = 16; c = -22;
Δ = b2-4ac
Δ = 162-4·(-2)·(-22)
Δ = 80
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{5}}{2*-2}=\frac{-16-4\sqrt{5}}{-4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{5}}{2*-2}=\frac{-16+4\sqrt{5}}{-4} $
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