76=2(x*x)+3x-5

Solution for 76=2(x*x)+3x-5 equation:

76=2(x*x)+3x-5

We move all terms to the left:

76-(2(x*x)+3x-5)=0

We add all the numbers together, and all the variables

-(2(+x*x)+3x-5)+76=0


We calculate terms in parentheses: -(2(+x*x)+3x-5), so:

2(+x*x)+3x-5

We add all the numbers together, and all the variables

3x+2(+x*x)-5

We multiply parentheses

2x^2+3x-5

Back to the equation:

-(2x^2+3x-5)


We get rid of parentheses

-2x^2-3x+5+76=0

We add all the numbers together, and all the variables

-2x^2-3x+81=0

a = -2; b = -3; c = +81;
Δ = b2-4ac
Δ = -32-4·(-2)·81
Δ = 657
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:

$\sqrt{\Delta}=\sqrt{657}=\sqrt{9*73}=\sqrt{9}*\sqrt{73}=3\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{73}}{2*-2}=\frac{3-3\sqrt{73}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{73}}{2*-2}=\frac{3+3\sqrt{73}}{-4}
$