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-9x-2x(x-9)=-8(x+9)+3
We move all terms to the left:
-9x-2x(x-9)-(-8(x+9)+3)=0
We multiply parentheses
-2x^2-9x+18x-(-8(x+9)+3)=0
We calculate terms in parentheses: -(-8(x+9)+3), so:We add all the numbers together, and all the variables
-8(x+9)+3
We multiply parentheses
-8x-72+3
We add all the numbers together, and all the variables
-8x-69
Back to the equation:
-(-8x-69)
-2x^2+9x-(-8x-69)=0
We get rid of parentheses
-2x^2+9x+8x+69=0
We add all the numbers together, and all the variables
-2x^2+17x+69=0
a = -2; b = 17; c = +69;
Δ = b2-4ac
Δ = 172-4·(-2)·69
Δ = 841
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{841}=29$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-29}{2*-2}=\frac{-46}{-4} =11+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+29}{2*-2}=\frac{12}{-4} =-3 $
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