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(5x-3)(5x-3)-(4x-6)(5x+6)=145
We move all terms to the left:
(5x-3)(5x-3)-(4x-6)(5x+6)-(145)=0
We multiply parentheses ..
(+25x^2-15x-15x+9)-(4x-6)(5x+6)-145=0
We get rid of parentheses
25x^2-15x-15x-(4x-6)(5x+6)+9-145=0
We multiply parentheses ..
25x^2-(+20x^2+24x-30x-36)-15x-15x+9-145=0
We add all the numbers together, and all the variables
25x^2-(+20x^2+24x-30x-36)-30x-136=0
We get rid of parentheses
25x^2-20x^2-24x+30x-30x+36-136=0
We add all the numbers together, and all the variables
5x^2-24x-100=0
a = 5; b = -24; c = -100;
Δ = b2-4ac
Δ = -242-4·5·(-100)
Δ = 2576
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2576}=\sqrt{16*161}=\sqrt{16}*\sqrt{161}=4\sqrt{161}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{161}}{2*5}=\frac{24-4\sqrt{161}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{161}}{2*5}=\frac{24+4\sqrt{161}}{10} $
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