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(5x-2)(5x+3)=62
We move all terms to the left:
(5x-2)(5x+3)-(62)=0
We multiply parentheses ..
(+25x^2+15x-10x-6)-62=0
We get rid of parentheses
25x^2+15x-10x-6-62=0
We add all the numbers together, and all the variables
25x^2+5x-68=0
a = 25; b = 5; c = -68;
Δ = b2-4ac
Δ = 52-4·25·(-68)
Δ = 6825
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6825}=\sqrt{25*273}=\sqrt{25}*\sqrt{273}=5\sqrt{273}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{273}}{2*25}=\frac{-5-5\sqrt{273}}{50} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{273}}{2*25}=\frac{-5+5\sqrt{273}}{50} $
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