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(4x+4)(x+4)=174
We move all terms to the left:
(4x+4)(x+4)-(174)=0
We multiply parentheses ..
(+4x^2+16x+4x+16)-174=0
We get rid of parentheses
4x^2+16x+4x+16-174=0
We add all the numbers together, and all the variables
4x^2+20x-158=0
a = 4; b = 20; c = -158;
Δ = b2-4ac
Δ = 202-4·4·(-158)
Δ = 2928
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2928}=\sqrt{16*183}=\sqrt{16}*\sqrt{183}=4\sqrt{183}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{183}}{2*4}=\frac{-20-4\sqrt{183}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{183}}{2*4}=\frac{-20+4\sqrt{183}}{8} $
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