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(6x-25)(4x+15)=18-
We move all terms to the left:
(6x-25)(4x+15)-(18-)=0
We add all the numbers together, and all the variables
(6x-25)(4x+15)-0=0
We add all the numbers together, and all the variables
(6x-25)(4x+15)=0
We multiply parentheses ..
(+24x^2+90x-100x-375)=0
We get rid of parentheses
24x^2+90x-100x-375=0
We add all the numbers together, and all the variables
24x^2-10x-375=0
a = 24; b = -10; c = -375;
Δ = b2-4ac
Δ = -102-4·24·(-375)
Δ = 36100
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{36100}=190$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-190}{2*24}=\frac{-180}{48} =-3+3/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+190}{2*24}=\frac{200}{48} =4+1/6 $
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