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(5x-2)(x+3)-(2x+7)(5x-2)=0
We multiply parentheses ..
(+5x^2+15x-2x-6)-(2x+7)(5x-2)=0
We get rid of parentheses
5x^2+15x-2x-(2x+7)(5x-2)-6=0
We multiply parentheses ..
5x^2-(+10x^2-4x+35x-14)+15x-2x-6=0
We add all the numbers together, and all the variables
5x^2-(+10x^2-4x+35x-14)+13x-6=0
We get rid of parentheses
5x^2-10x^2+4x-35x+13x+14-6=0
We add all the numbers together, and all the variables
-5x^2-18x+8=0
a = -5; b = -18; c = +8;
Δ = b2-4ac
Δ = -182-4·(-5)·8
Δ = 484
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{484}=22$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-22}{2*-5}=\frac{-4}{-10} =2/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+22}{2*-5}=\frac{40}{-10} =-4 $
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