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2x(2x-5)=3x+x-2
We move all terms to the left:
2x(2x-5)-(3x+x-2)=0
We add all the numbers together, and all the variables
2x(2x-5)-(4x-2)=0
We multiply parentheses
4x^2-10x-(4x-2)=0
We get rid of parentheses
4x^2-10x-4x+2=0
We add all the numbers together, and all the variables
4x^2-14x+2=0
a = 4; b = -14; c = +2;
Δ = b2-4ac
Δ = -142-4·4·2
Δ = 164
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{41}}{2*4}=\frac{14-2\sqrt{41}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{41}}{2*4}=\frac{14+2\sqrt{41}}{8} $
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