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8(1+2x)7x=153
We move all terms to the left:
8(1+2x)7x-(153)=0
We add all the numbers together, and all the variables
8(2x+1)7x-153=0
We multiply parentheses
112x^2+56x-153=0
a = 112; b = 56; c = -153;
Δ = b2-4ac
Δ = 562-4·112·(-153)
Δ = 71680
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{71680}=\sqrt{1024*70}=\sqrt{1024}*\sqrt{70}=32\sqrt{70}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-32\sqrt{70}}{2*112}=\frac{-56-32\sqrt{70}}{224} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+32\sqrt{70}}{2*112}=\frac{-56+32\sqrt{70}}{224} $
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