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(5x+13)(3x+8)=0
We multiply parentheses ..
(+15x^2+40x+39x+104)=0
We get rid of parentheses
15x^2+40x+39x+104=0
We add all the numbers together, and all the variables
15x^2+79x+104=0
a = 15; b = 79; c = +104;
Δ = b2-4ac
Δ = 792-4·15·104
Δ = 1
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{1}=1$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(79)-1}{2*15}=\frac{-80}{30} =-2+2/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(79)+1}{2*15}=\frac{-78}{30} =-2+3/5 $
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