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(X-2)(-2X-8)=6X-9
We move all terms to the left:
(X-2)(-2X-8)-(6X-9)=0
We get rid of parentheses
(X-2)(-2X-8)-6X+9=0
We multiply parentheses ..
(-2X^2-8X+4X+16)-6X+9=0
We get rid of parentheses
-2X^2-8X+4X-6X+16+9=0
We add all the numbers together, and all the variables
-2X^2-10X+25=0
a = -2; b = -10; c = +25;
Δ = b2-4ac
Δ = -102-4·(-2)·25
Δ = 300
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{3}}{2*-2}=\frac{10-10\sqrt{3}}{-4} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{3}}{2*-2}=\frac{10+10\sqrt{3}}{-4} $
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