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(5x+4)(6x-9)=83
We move all terms to the left:
(5x+4)(6x-9)-(83)=0
We multiply parentheses ..
(+30x^2-45x+24x-36)-83=0
We get rid of parentheses
30x^2-45x+24x-36-83=0
We add all the numbers together, and all the variables
30x^2-21x-119=0
a = 30; b = -21; c = -119;
Δ = b2-4ac
Δ = -212-4·30·(-119)
Δ = 14721
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{-(-21)-\sqrt{14721}}{2*30}=\frac{21-\sqrt{14721}}{60} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{14721}}{2*30}=\frac{21+\sqrt{14721}}{60} $
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