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-4x(1.5x-5)+4x=26
We move all terms to the left:
-4x(1.5x-5)+4x-(26)=0
We add all the numbers together, and all the variables
4x-4x(1.5x-5)-26=0
We multiply parentheses
-4x^2+4x+20x-26=0
We add all the numbers together, and all the variables
-4x^2+24x-26=0
a = -4; b = 24; c = -26;
Δ = b2-4ac
Δ = 242-4·(-4)·(-26)
Δ = 160
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{10}}{2*-4}=\frac{-24-4\sqrt{10}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{10}}{2*-4}=\frac{-24+4\sqrt{10}}{-8} $
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