4x^2=76-18x

Solution for 4x^2=76-18x equation:

4x^2=76-18x

We move all terms to the left:

4x^2-(76-18x)=0

We add all the numbers together, and all the variables

4x^2-(-18x+76)=0

We get rid of parentheses

4x^2+18x-76=0

a = 4; b = 18; c = -76;
Δ = b2-4ac
Δ = 182-4·4·(-76)
Δ = 1540
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:

$\sqrt{\Delta}=\sqrt{1540}=\sqrt{4*385}=\sqrt{4}*\sqrt{385}=2\sqrt{385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{385}}{2*4}=\frac{-18-2\sqrt{385}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{385}}{2*4}=\frac{-18+2\sqrt{385}}{8}
$