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3x(4x+5)=6
We move all terms to the left:
3x(4x+5)-(6)=0
We multiply parentheses
12x^2+15x-6=0
a = 12; b = 15; c = -6;
Δ = b2-4ac
Δ = 152-4·12·(-6)
Δ = 513
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{57}}{2*12}=\frac{-15-3\sqrt{57}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{57}}{2*12}=\frac{-15+3\sqrt{57}}{24} $
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