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(9x-5)(5x-12)=133
We move all terms to the left:
(9x-5)(5x-12)-(133)=0
We multiply parentheses ..
(+45x^2-108x-25x+60)-133=0
We get rid of parentheses
45x^2-108x-25x+60-133=0
We add all the numbers together, and all the variables
45x^2-133x-73=0
a = 45; b = -133; c = -73;
Δ = b2-4ac
Δ = -1332-4·45·(-73)
Δ = 30829
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{-(-133)-\sqrt{30829}}{2*45}=\frac{133-\sqrt{30829}}{90} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-133)+\sqrt{30829}}{2*45}=\frac{133+\sqrt{30829}}{90} $
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