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48+(2x*2x)=(2x+6)*4x
We move all terms to the left:
48+(2x*2x)-((2x+6)*4x)=0
We add all the numbers together, and all the variables
(+2x*2x)-((2x+6)*4x)+48=0
We get rid of parentheses
2x*2x-((2x+6)*4x)+48=0
We calculate terms in parentheses: -((2x+6)*4x), so:Wy multiply elements
(2x+6)*4x
We multiply parentheses
8x^2+24x
Back to the equation:
-(8x^2+24x)
4x^2-(8x^2+24x)+48=0
We get rid of parentheses
4x^2-8x^2-24x+48=0
We add all the numbers together, and all the variables
-4x^2-24x+48=0
a = -4; b = -24; c = +48;
Δ = b2-4ac
Δ = -242-4·(-4)·48
Δ = 1344
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{21}}{2*-4}=\frac{24-8\sqrt{21}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{21}}{2*-4}=\frac{24+8\sqrt{21}}{-8} $
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