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4(x+12)2x=6x+48
We move all terms to the left:
4(x+12)2x-(6x+48)=0
We multiply parentheses
8x^2+96x-(6x+48)=0
We get rid of parentheses
8x^2+96x-6x-48=0
We add all the numbers together, and all the variables
8x^2+90x-48=0
a = 8; b = 90; c = -48;
Δ = b2-4ac
Δ = 902-4·8·(-48)
Δ = 9636
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9636}=\sqrt{4*2409}=\sqrt{4}*\sqrt{2409}=2\sqrt{2409}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-2\sqrt{2409}}{2*8}=\frac{-90-2\sqrt{2409}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+2\sqrt{2409}}{2*8}=\frac{-90+2\sqrt{2409}}{16} $
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