85x*(-29.51x)=5x-4

Solution for 85x*(-29.51x)=5x-4 equation:

85x*(-29.51x)=5x-4

We move all terms to the left:

85x*(-29.51x)-(5x-4)=0

We multiply parentheses

-2465x^2-(5x-4)=0

We get rid of parentheses

-2465x^2-5x+4=0

a = -2465; b = -5; c = +4;
Δ = b2-4ac
Δ = -52-4·(-2465)·4
Δ = 39465
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:

$\sqrt{\Delta}=\sqrt{39465}=\sqrt{9*4385}=\sqrt{9}*\sqrt{4385}=3\sqrt{4385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{4385}}{2*-2465}=\frac{5-3\sqrt{4385}}{-4930}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{4385}}{2*-2465}=\frac{5+3\sqrt{4385}}{-4930}
$