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(4x-15)(x-6)=684
We move all terms to the left:
(4x-15)(x-6)-(684)=0
We multiply parentheses ..
(+4x^2-24x-15x+90)-684=0
We get rid of parentheses
4x^2-24x-15x+90-684=0
We add all the numbers together, and all the variables
4x^2-39x-594=0
a = 4; b = -39; c = -594;
Δ = b2-4ac
Δ = -392-4·4·(-594)
Δ = 11025
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{11025}=105$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-105}{2*4}=\frac{-66}{8} =-8+1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+105}{2*4}=\frac{144}{8} =18 $
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