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4x(3x+13)=8
We move all terms to the left:
4x(3x+13)-(8)=0
We multiply parentheses
12x^2+52x-8=0
a = 12; b = 52; c = -8;
Δ = b2-4ac
Δ = 522-4·12·(-8)
Δ = 3088
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3088}=\sqrt{16*193}=\sqrt{16}*\sqrt{193}=4\sqrt{193}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-4\sqrt{193}}{2*12}=\frac{-52-4\sqrt{193}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+4\sqrt{193}}{2*12}=\frac{-52+4\sqrt{193}}{24} $
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