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(2x+5)(4x-1)=108
We move all terms to the left:
(2x+5)(4x-1)-(108)=0
We multiply parentheses ..
(+8x^2-2x+20x-5)-108=0
We get rid of parentheses
8x^2-2x+20x-5-108=0
We add all the numbers together, and all the variables
8x^2+18x-113=0
a = 8; b = 18; c = -113;
Δ = b2-4ac
Δ = 182-4·8·(-113)
Δ = 3940
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3940}=\sqrt{4*985}=\sqrt{4}*\sqrt{985}=2\sqrt{985}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{985}}{2*8}=\frac{-18-2\sqrt{985}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{985}}{2*8}=\frac{-18+2\sqrt{985}}{16} $
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