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(6x-14)+(2x+16)(2x+8)=180
We move all terms to the left:
(6x-14)+(2x+16)(2x+8)-(180)=0
We get rid of parentheses
6x+(2x+16)(2x+8)-14-180=0
We multiply parentheses ..
(+4x^2+16x+32x+128)+6x-14-180=0
We add all the numbers together, and all the variables
(+4x^2+16x+32x+128)+6x-194=0
We get rid of parentheses
4x^2+16x+32x+6x+128-194=0
We add all the numbers together, and all the variables
4x^2+54x-66=0
a = 4; b = 54; c = -66;
Δ = b2-4ac
Δ = 542-4·4·(-66)
Δ = 3972
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3972}=\sqrt{4*993}=\sqrt{4}*\sqrt{993}=2\sqrt{993}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{993}}{2*4}=\frac{-54-2\sqrt{993}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{993}}{2*4}=\frac{-54+2\sqrt{993}}{8} $
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