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(2x+3)(4x+7)=200
We move all terms to the left:
(2x+3)(4x+7)-(200)=0
We multiply parentheses ..
(+8x^2+14x+12x+21)-200=0
We get rid of parentheses
8x^2+14x+12x+21-200=0
We add all the numbers together, and all the variables
8x^2+26x-179=0
a = 8; b = 26; c = -179;
Δ = b2-4ac
Δ = 262-4·8·(-179)
Δ = 6404
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6404}=\sqrt{4*1601}=\sqrt{4}*\sqrt{1601}=2\sqrt{1601}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{1601}}{2*8}=\frac{-26-2\sqrt{1601}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{1601}}{2*8}=\frac{-26+2\sqrt{1601}}{16} $
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