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2x(-5+6x)+10x(8-5x)=0
We add all the numbers together, and all the variables
2x(6x-5)+10x(-5x+8)=0
We multiply parentheses
12x^2-50x^2-10x+80x=0
We add all the numbers together, and all the variables
-38x^2+70x=0
a = -38; b = 70; c = 0;
Δ = b2-4ac
Δ = 702-4·(-38)·0
Δ = 4900
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{4900}=70$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-70}{2*-38}=\frac{-140}{-76} =1+16/19 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+70}{2*-38}=\frac{0}{-76} =0 $
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