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(3x+5)(x-2)=4
We move all terms to the left:
(3x+5)(x-2)-(4)=0
We multiply parentheses ..
(+3x^2-6x+5x-10)-4=0
We get rid of parentheses
3x^2-6x+5x-10-4=0
We add all the numbers together, and all the variables
3x^2-1x-14=0
a = 3; b = -1; c = -14;
Δ = b2-4ac
Δ = -12-4·3·(-14)
Δ = 169
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{169}=13$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-13}{2*3}=\frac{-12}{6} =-2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+13}{2*3}=\frac{14}{6} =2+1/3 $
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