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6x^2+24x=7x+8
We move all terms to the left:
6x^2+24x-(7x+8)=0
We get rid of parentheses
6x^2+24x-7x-8=0
We add all the numbers together, and all the variables
6x^2+17x-8=0
a = 6; b = 17; c = -8;
Δ = b2-4ac
Δ = 172-4·6·(-8)
Δ = 481
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-\sqrt{481}}{2*6}=\frac{-17-\sqrt{481}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{481}}{2*6}=\frac{-17+\sqrt{481}}{12} $
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