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(2x+3)(3x+2)=90
We move all terms to the left:
(2x+3)(3x+2)-(90)=0
We multiply parentheses ..
(+6x^2+4x+9x+6)-90=0
We get rid of parentheses
6x^2+4x+9x+6-90=0
We add all the numbers together, and all the variables
6x^2+13x-84=0
a = 6; b = 13; c = -84;
Δ = b2-4ac
Δ = 132-4·6·(-84)
Δ = 2185
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{-(13)-\sqrt{2185}}{2*6}=\frac{-13-\sqrt{2185}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{2185}}{2*6}=\frac{-13+\sqrt{2185}}{12} $
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