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4x(3x+2)=116
We move all terms to the left:
4x(3x+2)-(116)=0
We multiply parentheses
12x^2+8x-116=0
a = 12; b = 8; c = -116;
Δ = b2-4ac
Δ = 82-4·12·(-116)
Δ = 5632
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5632}=\sqrt{256*22}=\sqrt{256}*\sqrt{22}=16\sqrt{22}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-16\sqrt{22}}{2*12}=\frac{-8-16\sqrt{22}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+16\sqrt{22}}{2*12}=\frac{-8+16\sqrt{22}}{24} $
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