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(4x+3)(2x+1)=54
We move all terms to the left:
(4x+3)(2x+1)-(54)=0
We multiply parentheses ..
(+8x^2+4x+6x+3)-54=0
We get rid of parentheses
8x^2+4x+6x+3-54=0
We add all the numbers together, and all the variables
8x^2+10x-51=0
a = 8; b = 10; c = -51;
Δ = b2-4ac
Δ = 102-4·8·(-51)
Δ = 1732
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1732}=\sqrt{4*433}=\sqrt{4}*\sqrt{433}=2\sqrt{433}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{433}}{2*8}=\frac{-10-2\sqrt{433}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{433}}{2*8}=\frac{-10+2\sqrt{433}}{16} $
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