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(2x-4)(4x+10)=9x-9
We move all terms to the left:
(2x-4)(4x+10)-(9x-9)=0
We get rid of parentheses
(2x-4)(4x+10)-9x+9=0
We multiply parentheses ..
(+8x^2+20x-16x-40)-9x+9=0
We get rid of parentheses
8x^2+20x-16x-9x-40+9=0
We add all the numbers together, and all the variables
8x^2-5x-31=0
a = 8; b = -5; c = -31;
Δ = b2-4ac
Δ = -52-4·8·(-31)
Δ = 1017
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1017}=\sqrt{9*113}=\sqrt{9}*\sqrt{113}=3\sqrt{113}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{113}}{2*8}=\frac{5-3\sqrt{113}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{113}}{2*8}=\frac{5+3\sqrt{113}}{16} $
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