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(2x+5)(3x-2)+2(3x-2)=25
We move all terms to the left:
(2x+5)(3x-2)+2(3x-2)-(25)=0
We multiply parentheses
(2x+5)(3x-2)+6x-4-25=0
We multiply parentheses ..
(+6x^2-4x+15x-10)+6x-4-25=0
We add all the numbers together, and all the variables
(+6x^2-4x+15x-10)+6x-29=0
We get rid of parentheses
6x^2-4x+15x+6x-10-29=0
We add all the numbers together, and all the variables
6x^2+17x-39=0
a = 6; b = 17; c = -39;
Δ = b2-4ac
Δ = 172-4·6·(-39)
Δ = 1225
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{1225}=35$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-35}{2*6}=\frac{-52}{12} =-4+1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+35}{2*6}=\frac{18}{12} =1+1/2 $
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