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10x(x+2)-5x=-9x+16
We move all terms to the left:
10x(x+2)-5x-(-9x+16)=0
We add all the numbers together, and all the variables
-5x+10x(x+2)-(-9x+16)=0
We multiply parentheses
10x^2-5x+20x-(-9x+16)=0
We get rid of parentheses
10x^2-5x+20x+9x-16=0
We add all the numbers together, and all the variables
10x^2+24x-16=0
a = 10; b = 24; c = -16;
Δ = b2-4ac
Δ = 242-4·10·(-16)
Δ = 1216
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1216}=\sqrt{64*19}=\sqrt{64}*\sqrt{19}=8\sqrt{19}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{19}}{2*10}=\frac{-24-8\sqrt{19}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{19}}{2*10}=\frac{-24+8\sqrt{19}}{20} $
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