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(5x+3)(2x+7)=
We move all terms to the left:
(5x+3)(2x+7)-()=0
We add all the numbers together, and all the variables
(5x+3)(2x+7)=0
We multiply parentheses ..
(+10x^2+35x+6x+21)=0
We get rid of parentheses
10x^2+35x+6x+21=0
We add all the numbers together, and all the variables
10x^2+41x+21=0
a = 10; b = 41; c = +21;
Δ = b2-4ac
Δ = 412-4·10·21
Δ = 841
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{841}=29$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-29}{2*10}=\frac{-70}{20} =-3+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+29}{2*10}=\frac{-12}{20} =-3/5 $
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