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5x(2x-7)=15x-10
We move all terms to the left:
5x(2x-7)-(15x-10)=0
We multiply parentheses
10x^2-35x-(15x-10)=0
We get rid of parentheses
10x^2-35x-15x+10=0
We add all the numbers together, and all the variables
10x^2-50x+10=0
a = 10; b = -50; c = +10;
Δ = b2-4ac
Δ = -502-4·10·10
Δ = 2100
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2100}=\sqrt{100*21}=\sqrt{100}*\sqrt{21}=10\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{21}}{2*10}=\frac{50-10\sqrt{21}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{21}}{2*10}=\frac{50+10\sqrt{21}}{20} $
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