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3x^2+14x-24=4x-2
We move all terms to the left:
3x^2+14x-24-(4x-2)=0
We get rid of parentheses
3x^2+14x-4x+2-24=0
We add all the numbers together, and all the variables
3x^2+10x-22=0
a = 3; b = 10; c = -22;
Δ = b2-4ac
Δ = 102-4·3·(-22)
Δ = 364
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{91}}{2*3}=\frac{-10-2\sqrt{91}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{91}}{2*3}=\frac{-10+2\sqrt{91}}{6} $
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