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4x(10-x)=46-6x
We move all terms to the left:
4x(10-x)-(46-6x)=0
We add all the numbers together, and all the variables
4x(-1x+10)-(-6x+46)=0
We multiply parentheses
-4x^2+40x-(-6x+46)=0
We get rid of parentheses
-4x^2+40x+6x-46=0
We add all the numbers together, and all the variables
-4x^2+46x-46=0
a = -4; b = 46; c = -46;
Δ = b2-4ac
Δ = 462-4·(-4)·(-46)
Δ = 1380
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1380}=\sqrt{4*345}=\sqrt{4}*\sqrt{345}=2\sqrt{345}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-2\sqrt{345}}{2*-4}=\frac{-46-2\sqrt{345}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+2\sqrt{345}}{2*-4}=\frac{-46+2\sqrt{345}}{-8} $
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