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(9x-16)(3x+11)=7x-5
We move all terms to the left:
(9x-16)(3x+11)-(7x-5)=0
We get rid of parentheses
(9x-16)(3x+11)-7x+5=0
We multiply parentheses ..
(+27x^2+99x-48x-176)-7x+5=0
We get rid of parentheses
27x^2+99x-48x-7x-176+5=0
We add all the numbers together, and all the variables
27x^2+44x-171=0
a = 27; b = 44; c = -171;
Δ = b2-4ac
Δ = 442-4·27·(-171)
Δ = 20404
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{20404}=\sqrt{4*5101}=\sqrt{4}*\sqrt{5101}=2\sqrt{5101}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-2\sqrt{5101}}{2*27}=\frac{-44-2\sqrt{5101}}{54} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+2\sqrt{5101}}{2*27}=\frac{-44+2\sqrt{5101}}{54} $
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