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(5x+4)3x=29
We move all terms to the left:
(5x+4)3x-(29)=0
We multiply parentheses
15x^2+12x-29=0
a = 15; b = 12; c = -29;
Δ = b2-4ac
Δ = 122-4·15·(-29)
Δ = 1884
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1884}=\sqrt{4*471}=\sqrt{4}*\sqrt{471}=2\sqrt{471}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{471}}{2*15}=\frac{-12-2\sqrt{471}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{471}}{2*15}=\frac{-12+2\sqrt{471}}{30} $
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