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9x^2+2x-11=5x/16
We move all terms to the left:
9x^2+2x-11-(5x/16)=0
We add all the numbers together, and all the variables
9x^2+2x-(+5x/16)-11=0
We get rid of parentheses
9x^2+2x-5x/16-11=0
We multiply all the terms by the denominator
9x^2*16+2x*16-5x-11*16=0
We add all the numbers together, and all the variables
9x^2*16-5x+2x*16-176=0
Wy multiply elements
144x^2-5x+32x-176=0
We add all the numbers together, and all the variables
144x^2+27x-176=0
a = 144; b = 27; c = -176;
Δ = b2-4ac
Δ = 272-4·144·(-176)
Δ = 102105
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{102105}=\sqrt{9*11345}=\sqrt{9}*\sqrt{11345}=3\sqrt{11345}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{11345}}{2*144}=\frac{-27-3\sqrt{11345}}{288} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{11345}}{2*144}=\frac{-27+3\sqrt{11345}}{288} $
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