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(2x-3)(5x+1)=2x+7
We move all terms to the left:
(2x-3)(5x+1)-(2x+7)=0
We get rid of parentheses
(2x-3)(5x+1)-2x-7=0
We multiply parentheses ..
(+10x^2+2x-15x-3)-2x-7=0
We get rid of parentheses
10x^2+2x-15x-2x-3-7=0
We add all the numbers together, and all the variables
10x^2-15x-10=0
a = 10; b = -15; c = -10;
Δ = b2-4ac
Δ = -152-4·10·(-10)
Δ = 625
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{625}=25$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-25}{2*10}=\frac{-10}{20} =-1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+25}{2*10}=\frac{40}{20} =2 $
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