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4x(12+12x)+8(14+10x)=800
We move all terms to the left:
4x(12+12x)+8(14+10x)-(800)=0
We add all the numbers together, and all the variables
4x(12x+12)+8(10x+14)-800=0
We multiply parentheses
48x^2+48x+80x+112-800=0
We add all the numbers together, and all the variables
48x^2+128x-688=0
a = 48; b = 128; c = -688;
Δ = b2-4ac
Δ = 1282-4·48·(-688)
Δ = 148480
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{148480}=\sqrt{1024*145}=\sqrt{1024}*\sqrt{145}=32\sqrt{145}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-32\sqrt{145}}{2*48}=\frac{-128-32\sqrt{145}}{96} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+32\sqrt{145}}{2*48}=\frac{-128+32\sqrt{145}}{96} $
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