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(5x-3)(5x-3)+2(5x-3)=x
We move all terms to the left:
(5x-3)(5x-3)+2(5x-3)-(x)=0
We add all the numbers together, and all the variables
-1x+(5x-3)(5x-3)+2(5x-3)=0
We multiply parentheses
-1x+(5x-3)(5x-3)+10x-6=0
We multiply parentheses ..
(+25x^2-15x-15x+9)-1x+10x-6=0
We add all the numbers together, and all the variables
(+25x^2-15x-15x+9)+9x-6=0
We get rid of parentheses
25x^2-15x-15x+9x+9-6=0
We add all the numbers together, and all the variables
25x^2-21x+3=0
a = 25; b = -21; c = +3;
Δ = b2-4ac
Δ = -212-4·25·3
Δ = 141
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{141}}{2*25}=\frac{21-\sqrt{141}}{50} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{141}}{2*25}=\frac{21+\sqrt{141}}{50} $
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