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(5x+12)(6x-11)=90
We move all terms to the left:
(5x+12)(6x-11)-(90)=0
We multiply parentheses ..
(+30x^2-55x+72x-132)-90=0
We get rid of parentheses
30x^2-55x+72x-132-90=0
We add all the numbers together, and all the variables
30x^2+17x-222=0
a = 30; b = 17; c = -222;
Δ = b2-4ac
Δ = 172-4·30·(-222)
Δ = 26929
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{-(17)-\sqrt{26929}}{2*30}=\frac{-17-\sqrt{26929}}{60} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{26929}}{2*30}=\frac{-17+\sqrt{26929}}{60} $
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