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5x+12=2x(5x+10)
We move all terms to the left:
5x+12-(2x(5x+10))=0
We calculate terms in parentheses: -(2x(5x+10)), so:We get rid of parentheses
2x(5x+10)
We multiply parentheses
10x^2+20x
Back to the equation:
-(10x^2+20x)
-10x^2+5x-20x+12=0
We add all the numbers together, and all the variables
-10x^2-15x+12=0
a = -10; b = -15; c = +12;
Δ = b2-4ac
Δ = -152-4·(-10)·12
Δ = 705
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{-(-15)-\sqrt{705}}{2*-10}=\frac{15-\sqrt{705}}{-20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{705}}{2*-10}=\frac{15+\sqrt{705}}{-20} $
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