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(3x+4)(6x+5)=464
We move all terms to the left:
(3x+4)(6x+5)-(464)=0
We multiply parentheses ..
(+18x^2+15x+24x+20)-464=0
We get rid of parentheses
18x^2+15x+24x+20-464=0
We add all the numbers together, and all the variables
18x^2+39x-444=0
a = 18; b = 39; c = -444;
Δ = b2-4ac
Δ = 392-4·18·(-444)
Δ = 33489
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{33489}=183$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-183}{2*18}=\frac{-222}{36} =-6+1/6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+183}{2*18}=\frac{144}{36} =4 $
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