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(2x+9)(5x-12)=360
We move all terms to the left:
(2x+9)(5x-12)-(360)=0
We multiply parentheses ..
(+10x^2-24x+45x-108)-360=0
We get rid of parentheses
10x^2-24x+45x-108-360=0
We add all the numbers together, and all the variables
10x^2+21x-468=0
a = 10; b = 21; c = -468;
Δ = b2-4ac
Δ = 212-4·10·(-468)
Δ = 19161
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{19161}=\sqrt{9*2129}=\sqrt{9}*\sqrt{2129}=3\sqrt{2129}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{2129}}{2*10}=\frac{-21-3\sqrt{2129}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{2129}}{2*10}=\frac{-21+3\sqrt{2129}}{20} $
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