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5x(3x-2)=4x+24
We move all terms to the left:
5x(3x-2)-(4x+24)=0
We multiply parentheses
15x^2-10x-(4x+24)=0
We get rid of parentheses
15x^2-10x-4x-24=0
We add all the numbers together, and all the variables
15x^2-14x-24=0
a = 15; b = -14; c = -24;
Δ = b2-4ac
Δ = -142-4·15·(-24)
Δ = 1636
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1636}=\sqrt{4*409}=\sqrt{4}*\sqrt{409}=2\sqrt{409}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{409}}{2*15}=\frac{14-2\sqrt{409}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{409}}{2*15}=\frac{14+2\sqrt{409}}{30} $
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