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(8x-3)(3x+5)=x-6
We move all terms to the left:
(8x-3)(3x+5)-(x-6)=0
We get rid of parentheses
(8x-3)(3x+5)-x+6=0
We multiply parentheses ..
(+24x^2+40x-9x-15)-x+6=0
We add all the numbers together, and all the variables
(+24x^2+40x-9x-15)-1x+6=0
We get rid of parentheses
24x^2+40x-9x-1x-15+6=0
We add all the numbers together, and all the variables
24x^2+30x-9=0
a = 24; b = 30; c = -9;
Δ = b2-4ac
Δ = 302-4·24·(-9)
Δ = 1764
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{1764}=42$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-42}{2*24}=\frac{-72}{48} =-1+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+42}{2*24}=\frac{12}{48} =1/4 $
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