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(5x-12)(6x+17)=0
We multiply parentheses ..
(+30x^2+85x-72x-204)=0
We get rid of parentheses
30x^2+85x-72x-204=0
We add all the numbers together, and all the variables
30x^2+13x-204=0
a = 30; b = 13; c = -204;
Δ = b2-4ac
Δ = 132-4·30·(-204)
Δ = 24649
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{24649}=157$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-157}{2*30}=\frac{-170}{60} =-2+5/6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+157}{2*30}=\frac{144}{60} =2+2/5 $
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