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(5x-6)(2x+9)=0
We multiply parentheses ..
(+10x^2+45x-12x-54)=0
We get rid of parentheses
10x^2+45x-12x-54=0
We add all the numbers together, and all the variables
10x^2+33x-54=0
a = 10; b = 33; c = -54;
Δ = b2-4ac
Δ = 332-4·10·(-54)
Δ = 3249
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{3249}=57$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-57}{2*10}=\frac{-90}{20} =-4+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+57}{2*10}=\frac{24}{20} =1+1/5 $
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