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(5x+7)(2x+3)-(5x+7)(5x+7)=0
We multiply parentheses ..
(+10x^2+15x+14x+21)-(5x+7)(5x+7)=0
We get rid of parentheses
10x^2+15x+14x-(5x+7)(5x+7)+21=0
We multiply parentheses ..
10x^2-(+25x^2+35x+35x+49)+15x+14x+21=0
We add all the numbers together, and all the variables
10x^2-(+25x^2+35x+35x+49)+29x+21=0
We get rid of parentheses
10x^2-25x^2-35x-35x+29x-49+21=0
We add all the numbers together, and all the variables
-15x^2-41x-28=0
a = -15; b = -41; c = -28;
Δ = b2-4ac
Δ = -412-4·(-15)·(-28)
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-1}{2*-15}=\frac{40}{-30} =-1+1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+1}{2*-15}=\frac{42}{-30} =-1+2/5 $
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