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9x^2+10x=17/4
We move all terms to the left:
9x^2+10x-(17/4)=0
We add all the numbers together, and all the variables
9x^2+10x-(+17/4)=0
We get rid of parentheses
9x^2+10x-17/4=0
We multiply all the terms by the denominator
9x^2*4+10x*4-17=0
Wy multiply elements
36x^2+40x-17=0
a = 36; b = 40; c = -17;
Δ = b2-4ac
Δ = 402-4·36·(-17)
Δ = 4048
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4048}=\sqrt{16*253}=\sqrt{16}*\sqrt{253}=4\sqrt{253}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{253}}{2*36}=\frac{-40-4\sqrt{253}}{72} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{253}}{2*36}=\frac{-40+4\sqrt{253}}{72} $
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