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(3x+1)*2x=7.5
We move all terms to the left:
(3x+1)*2x-(7.5)=0
We add all the numbers together, and all the variables
(3x+1)*2x-7.5=0
We multiply parentheses
6x^2+2x-7.5=0
a = 6; b = 2; c = -7.5;
Δ = b2-4ac
Δ = 22-4·6·(-7.5)
Δ = 184
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{46}}{2*6}=\frac{-2-2\sqrt{46}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{46}}{2*6}=\frac{-2+2\sqrt{46}}{12} $
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