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(X+4)(2X+4)=169
We move all terms to the left:
(X+4)(2X+4)-(169)=0
We multiply parentheses ..
(+2X^2+4X+8X+16)-169=0
We get rid of parentheses
2X^2+4X+8X+16-169=0
We add all the numbers together, and all the variables
2X^2+12X-153=0
a = 2; b = 12; c = -153;
Δ = b2-4ac
Δ = 122-4·2·(-153)
Δ = 1368
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1368}=\sqrt{36*38}=\sqrt{36}*\sqrt{38}=6\sqrt{38}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{38}}{2*2}=\frac{-12-6\sqrt{38}}{4} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{38}}{2*2}=\frac{-12+6\sqrt{38}}{4} $
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