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(8x-24)(6x+10)=40
We move all terms to the left:
(8x-24)(6x+10)-(40)=0
We multiply parentheses ..
(+48x^2+80x-144x-240)-40=0
We get rid of parentheses
48x^2+80x-144x-240-40=0
We add all the numbers together, and all the variables
48x^2-64x-280=0
a = 48; b = -64; c = -280;
Δ = b2-4ac
Δ = -642-4·48·(-280)
Δ = 57856
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{57856}=\sqrt{256*226}=\sqrt{256}*\sqrt{226}=16\sqrt{226}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-16\sqrt{226}}{2*48}=\frac{64-16\sqrt{226}}{96} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+16\sqrt{226}}{2*48}=\frac{64+16\sqrt{226}}{96} $
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