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(2x+11)(2x+5)=105
We move all terms to the left:
(2x+11)(2x+5)-(105)=0
We multiply parentheses ..
(+4x^2+10x+22x+55)-105=0
We get rid of parentheses
4x^2+10x+22x+55-105=0
We add all the numbers together, and all the variables
4x^2+32x-50=0
a = 4; b = 32; c = -50;
Δ = b2-4ac
Δ = 322-4·4·(-50)
Δ = 1824
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1824}=\sqrt{16*114}=\sqrt{16}*\sqrt{114}=4\sqrt{114}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{114}}{2*4}=\frac{-32-4\sqrt{114}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{114}}{2*4}=\frac{-32+4\sqrt{114}}{8} $
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