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5x(x-12)=2x-3
We move all terms to the left:
5x(x-12)-(2x-3)=0
We multiply parentheses
5x^2-60x-(2x-3)=0
We get rid of parentheses
5x^2-60x-2x+3=0
We add all the numbers together, and all the variables
5x^2-62x+3=0
a = 5; b = -62; c = +3;
Δ = b2-4ac
Δ = -622-4·5·3
Δ = 3784
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3784}=\sqrt{4*946}=\sqrt{4}*\sqrt{946}=2\sqrt{946}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-62)-2\sqrt{946}}{2*5}=\frac{62-2\sqrt{946}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-62)+2\sqrt{946}}{2*5}=\frac{62+2\sqrt{946}}{10} $
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