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(4x+2)(2x+5)=338
We move all terms to the left:
(4x+2)(2x+5)-(338)=0
We multiply parentheses ..
(+8x^2+20x+4x+10)-338=0
We get rid of parentheses
8x^2+20x+4x+10-338=0
We add all the numbers together, and all the variables
8x^2+24x-328=0
a = 8; b = 24; c = -328;
Δ = b2-4ac
Δ = 242-4·8·(-328)
Δ = 11072
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{11072}=\sqrt{64*173}=\sqrt{64}*\sqrt{173}=8\sqrt{173}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{173}}{2*8}=\frac{-24-8\sqrt{173}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{173}}{2*8}=\frac{-24+8\sqrt{173}}{16} $
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