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1080=(x+8)(2x+8)
We move all terms to the left:
1080-((x+8)(2x+8))=0
We multiply parentheses ..
-((+2x^2+8x+16x+64))+1080=0
We calculate terms in parentheses: -((+2x^2+8x+16x+64)), so:We get rid of parentheses
(+2x^2+8x+16x+64)
We get rid of parentheses
2x^2+8x+16x+64
We add all the numbers together, and all the variables
2x^2+24x+64
Back to the equation:
-(2x^2+24x+64)
-2x^2-24x-64+1080=0
We add all the numbers together, and all the variables
-2x^2-24x+1016=0
a = -2; b = -24; c = +1016;
Δ = b2-4ac
Δ = -242-4·(-2)·1016
Δ = 8704
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8704}=\sqrt{256*34}=\sqrt{256}*\sqrt{34}=16\sqrt{34}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-16\sqrt{34}}{2*-2}=\frac{24-16\sqrt{34}}{-4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+16\sqrt{34}}{2*-2}=\frac{24+16\sqrt{34}}{-4} $
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