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(2x+10)(2x+7)+4x=342
We move all terms to the left:
(2x+10)(2x+7)+4x-(342)=0
We add all the numbers together, and all the variables
4x+(2x+10)(2x+7)-342=0
We multiply parentheses ..
(+4x^2+14x+20x+70)+4x-342=0
We get rid of parentheses
4x^2+14x+20x+4x+70-342=0
We add all the numbers together, and all the variables
4x^2+38x-272=0
a = 4; b = 38; c = -272;
Δ = b2-4ac
Δ = 382-4·4·(-272)
Δ = 5796
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5796}=\sqrt{36*161}=\sqrt{36}*\sqrt{161}=6\sqrt{161}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-6\sqrt{161}}{2*4}=\frac{-38-6\sqrt{161}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+6\sqrt{161}}{2*4}=\frac{-38+6\sqrt{161}}{8} $
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