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(6x+5)(4x+15)=160
We move all terms to the left:
(6x+5)(4x+15)-(160)=0
We multiply parentheses ..
(+24x^2+90x+20x+75)-160=0
We get rid of parentheses
24x^2+90x+20x+75-160=0
We add all the numbers together, and all the variables
24x^2+110x-85=0
a = 24; b = 110; c = -85;
Δ = b2-4ac
Δ = 1102-4·24·(-85)
Δ = 20260
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{20260}=\sqrt{4*5065}=\sqrt{4}*\sqrt{5065}=2\sqrt{5065}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(110)-2\sqrt{5065}}{2*24}=\frac{-110-2\sqrt{5065}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(110)+2\sqrt{5065}}{2*24}=\frac{-110+2\sqrt{5065}}{48} $
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