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2x(5x+9)=10x+18
We move all terms to the left:
2x(5x+9)-(10x+18)=0
We multiply parentheses
10x^2+18x-(10x+18)=0
We get rid of parentheses
10x^2+18x-10x-18=0
We add all the numbers together, and all the variables
10x^2+8x-18=0
a = 10; b = 8; c = -18;
Δ = b2-4ac
Δ = 82-4·10·(-18)
Δ = 784
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{784}=28$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-28}{2*10}=\frac{-36}{20} =-1+4/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+28}{2*10}=\frac{20}{20} =1 $
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