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4x(3x-2)=52
We move all terms to the left:
4x(3x-2)-(52)=0
We multiply parentheses
12x^2-8x-52=0
a = 12; b = -8; c = -52;
Δ = b2-4ac
Δ = -82-4·12·(-52)
Δ = 2560
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2560}=\sqrt{256*10}=\sqrt{256}*\sqrt{10}=16\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-16\sqrt{10}}{2*12}=\frac{8-16\sqrt{10}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+16\sqrt{10}}{2*12}=\frac{8+16\sqrt{10}}{24} $
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