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2x(5x-4)=3x+10
We move all terms to the left:
2x(5x-4)-(3x+10)=0
We multiply parentheses
10x^2-8x-(3x+10)=0
We get rid of parentheses
10x^2-8x-3x-10=0
We add all the numbers together, and all the variables
10x^2-11x-10=0
a = 10; b = -11; c = -10;
Δ = b2-4ac
Δ = -112-4·10·(-10)
Δ = 521
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{521}}{2*10}=\frac{11-\sqrt{521}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{521}}{2*10}=\frac{11+\sqrt{521}}{20} $
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