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x=-4x^2+151x-760
We move all terms to the left:
x-(-4x^2+151x-760)=0
We get rid of parentheses
4x^2-151x+x+760=0
We add all the numbers together, and all the variables
4x^2-150x+760=0
a = 4; b = -150; c = +760;
Δ = b2-4ac
Δ = -1502-4·4·760
Δ = 10340
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{10340}=\sqrt{4*2585}=\sqrt{4}*\sqrt{2585}=2\sqrt{2585}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-2\sqrt{2585}}{2*4}=\frac{150-2\sqrt{2585}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+2\sqrt{2585}}{2*4}=\frac{150+2\sqrt{2585}}{8} $
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