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(5x+8)(6x+8)=82
We move all terms to the left:
(5x+8)(6x+8)-(82)=0
We multiply parentheses ..
(+30x^2+40x+48x+64)-82=0
We get rid of parentheses
30x^2+40x+48x+64-82=0
We add all the numbers together, and all the variables
30x^2+88x-18=0
a = 30; b = 88; c = -18;
Δ = b2-4ac
Δ = 882-4·30·(-18)
Δ = 9904
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9904}=\sqrt{16*619}=\sqrt{16}*\sqrt{619}=4\sqrt{619}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(88)-4\sqrt{619}}{2*30}=\frac{-88-4\sqrt{619}}{60} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(88)+4\sqrt{619}}{2*30}=\frac{-88+4\sqrt{619}}{60} $
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