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144=(5x-3)(5x-3)
We move all terms to the left:
144-((5x-3)(5x-3))=0
We multiply parentheses ..
-((+25x^2-15x-15x+9))+144=0
We calculate terms in parentheses: -((+25x^2-15x-15x+9)), so:We get rid of parentheses
(+25x^2-15x-15x+9)
We get rid of parentheses
25x^2-15x-15x+9
We add all the numbers together, and all the variables
25x^2-30x+9
Back to the equation:
-(25x^2-30x+9)
-25x^2+30x-9+144=0
We add all the numbers together, and all the variables
-25x^2+30x+135=0
a = -25; b = 30; c = +135;
Δ = b2-4ac
Δ = 302-4·(-25)·135
Δ = 14400
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{14400}=120$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-120}{2*-25}=\frac{-150}{-50} =+3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+120}{2*-25}=\frac{90}{-50} =-1+4/5 $
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