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(2x+1)(3x-1)=150
We move all terms to the left:
(2x+1)(3x-1)-(150)=0
We multiply parentheses ..
(+6x^2-2x+3x-1)-150=0
We get rid of parentheses
6x^2-2x+3x-1-150=0
We add all the numbers together, and all the variables
6x^2+x-151=0
a = 6; b = 1; c = -151;
Δ = b2-4ac
Δ = 12-4·6·(-151)
Δ = 3625
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3625}=\sqrt{25*145}=\sqrt{25}*\sqrt{145}=5\sqrt{145}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5\sqrt{145}}{2*6}=\frac{-1-5\sqrt{145}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5\sqrt{145}}{2*6}=\frac{-1+5\sqrt{145}}{12} $
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